Ok, no spell checking again, but with the content of this post I don't think that will matter much. Spelling is the least of my issues with this one.

Gun kata. From book 2 comes the ranged combat companion to the maneuvers in the first book.

They're mechancially nearly exactly the same as the sword schools. It's gunslinger level instead of initator level, trick shots instead of maneuvers, etc., etc. But other than the name changes it's all the same. Except. The sword school maneuvers are explicitly noted to not work with ranged weapons and there's something that the gun kata trick shots don't work with. I, personally, ignore that as a DM because the only overlap is in ordinary & syrnth weapons and I don't find the maneuver boosts to be problematic. In fact I think that the gun kata existing sort of prove that it's not a problem. Plus it lets the guardsman & fighter class tracks (both get iron heart which applies to ordinary weapons) have native access to, effectively, gun kata. Now gun kata not only don't apply to melee weapons, but they also don't apply to blast and flame weapons. So you can't use them with grenade launchers, missile launchers, or flamers. That's something I missed in the beginning, one of my players took a single level of a gun kata class to get a single level of gun kata, to apply... Well, I'll mention it when we get there.

Notably while the sword schools have some weak spots (like a bunch of lousy capstone moves for some reason) they aren't anything that I'd seriously consider to cause problems. There's at least two bits in the gun katas that I don't quite feel the same way about. Again, we'll get there.

Building trick shots works exactly the same as building maneuvers. Costs the same amount of xp, uses the same rules. They also have the same universal advantages and restrictions available. However, unless specifically noted all gun kata work with all ranged weapons (except blast wepons and flamers).

Clay pigeon gun kata.
L1: Called shots can be used with trick shots.
+1 advantage - the attack does not expend ammunition. This is one of the ones that gets iffy for me. I accidentally let it apply to missile launchers. That was a problem. Weirdly I would not have a problem with flamers or grenade launchers, just the missile launchers. Ah, well. I'm not sure about this one except that I feel that it comes too early and too cheaply.
L2: -1 restriction - the attack can only be used with pistols. So here's a thing that's different from sword schools. And it's definitely more powerful as you can apply any gun kata to any gun without restriction.
+2 advantage - on a hit the target drops anything they're holding.
L3: -1 restriction - make a performance check as part of the attack roll. Same as with maneuvers, DC is the target's static defense and failure means that you failed/missed the shot.
+1 advantage - on hit the targets are knocked prone.
L4: -1 restriction - the attack does no damage. It's a lousy restriction, you'll only use it with needlers which tend to underperform anyways if you aren't using them for sniping. Webbers have a blast radius. Maybe you really care about bolas for some reason?
Bonus - you can use ballistics + dexterity to parry ranged attacks instead of weaponry + dexterity. Except that ranged attacks can't normally be parried without a stunt and parrying uses weaponry + level(if proficient). So, editing mistake. Probably something left in from an earlier draft?
L5: +2 advantage - the attack ignores cover and concealment. Now, since we don't have quite the same level of precise definition as some games, and cover works a bit differently anyways, I would have appreciated a little more... Specificity? In what exactly this is supposed to mean.

Overall... Well you really really like level 1. Auto-disarm at level 2 is pretty good. After that I'm rather unimpressed untill level 5, and that's only because the level 5 ability is only a +2 advantage. In a sword school that's likely closer to a +4 advantage.

Dip-tastic. Probably not worth it for the long haul.

Crisis zone gun kata.
L1: First, no penalty for firing heavy wepons without bracing them (it's a half action). Pretty good.
Second, use trick shots with suppressing fire actions. Suppression is basically shooting vs DC 20 along a 45 degree spread at a kill zone. People in there make pinning (willpower, semi-fear like) tests and failure makes then have to move towards cover, plus some attack penalties. You also randomly tag one person plus another per +10 on the shooting roll. Great for breaking up formations of regular troops.
L2: -1 restriction - can only be used with heavy wepaons.
+1 advantage - if you hit allies who also hit can use the same hit location that you rolled.
L3: -1 restriction - roll tech use in addition to the attack roll.
+1 advantage (stacking) - weirdly this is written as a +X advantage, which is the same as a +1 stacking advantage. Targets hit by the attack have -1 penalty to their armor rating for one round. So, start of your next turn, end of your next turn, end of the round, the rest of this round and all of next round? And does it apply to this hits damage or does it apply after the hit? DM choices. Me? untill the beginning of your next round and applied to this hit's damage (so functions like extra penetration on this hit).
L4: +1 advantage - turn the ROF of a full auto weapon into the blast radius of the weapon. Doesn't make it an explosion though. So high ROF weapons could hit more people than rounds shot with this. Yes a ROF 10 full auto from a regular machine gun ends up with a 20m diameter blast that does regular impact damage from bullets to anyone/anything is the area, even of there are 40 people in there. Well, it's no crazier than how the minion rules work out sometimes.
+2 advantage - Ah, no bonus on this gun kata. On a hit the target loses a half action off of their next turn. Rough.
L5: +4 advantage - instead of full auto damage increasing by +1k0 per round that hits you get +2k0 per round that hits. Great if you can stick ten rounds on target, not so much if you can barely hit or have a ROF of 2 (double barreled shotguns use the full-auto rules, which works out ok).

So we've broken the bonus ability at level 4 pattern. This is a pretty good gun kata, although like clay pigeon the level 1 ability is great, 2 & 3 are kind of 'eh, whatever', and the end ones are ok to pretty good.

Elemental gearbolt gun kata.
L1: Choose your damage type when shooting. Just, you know, choose something, like, on the fly as you need it.
Use trick shots with multi-attack actions. That's dual weilding, double tap, fan the hammer, and I can't think of any others off the top of my head.
L2: -2 restriction - can only use primitive ballistic weapons with the attack. This actually includes muskets and other basic blackpowder firearms. Hm. There were blackpowder organ guns right?
+1 advantage - for each 1 that you roll on damage half the damage total, for each 10 double it. This doesn't say kept dice, so that's rolled dice? Tieflings reroll ones on damage rolls. How do you count those?
L3: -1 restriction - arcana roll as part of the attack roll.
+1 advantage (stacking) - again written as a +X advantage. The attack has no damage roll. For each point of this advantage the target loses that many wounds. Yeah, turn that 2k2 zero armor penetration pocket plinker into a "ignore armor and resilience, take 10 wounds" gun. Wait... We got up to a +18 on the knife throw maneuver. Yeah, this is a level 3 +1 advantage and I have a bridge in Brooklyn to sell you.
L4: -1 restriction - double the target's armor versus this attack. Hello, did you see what you gave us last level?
+1 advantage - if you miss, reroll the attack once. Nice, but what's that "once" doing in there? Did this stack at one point? Or is it not supposed to stack with other reroll abilities?
L5: +4 advantage - on a hit the traget begins bleeding. Which is a fair nasty condition, this is what I expect of a level 5 +4 advantage. Still, level 3 blows it away.

Power creep much? You'll take this to level 3, probably 4, not that level 1 wasn't pretty good already. Don't bother with level 5, just buy more "ignore all armor and resilience" from level 3 and blow holes through tanks. Right. After an errata for the spells I'll have to do the sword schools and gun kata too.

Point blank gun school.
L1: No penalties for shooting into melee. It wasn't a real harsh penalty anyways.
Use full auto with trick shots. Except of course that this isn't the full auto shooting gun kata, that was crisis zone.
L2: -1 restriction - the attack may only be used in melee.
+1 advantage - a target hit by this attack gains a level of fatigue. Good.
L3: -1 restriction - athletics roll as part of the attack roll.
+1 advantage - you may force a target hit by the attack to move in any direction. Up to their base speed of course. Nasty if there are cliffs or bottomless pits around.
L4: Bonus - you can parry using a gun and the ballistics skill instead of a the weaponry skill. I already allow the parry with a gun thing, but I have a check for damage to the gun unless it's a pretty good stunt.
Bonus bonus - What, they stole the crisis zone level 4 bonus and put it here? You can use basic typed weapons in melee combat... Ah, ok. The basic weapon proficency covers ordinary, laz, and primitive ranged weapons. Nope, nope, I was wrong. It's all non-pistol and non-heavy weapons... which would then include the thrown weapons that aren't explode(grenades).
L5: +4 advantage - make an extra unarmed attack as part of the attack. Well I hope you're a good strong brawler.

Yes take level 1, maybe 2. Ok, take level 3 if your DM likes bottomless pits and hazards. Otherwise... Meh? And not a single thing is particularly thematic with full auto attacks.

Silent scope gun kata. Sniper boy, you're up.
L1: Reduce the long and extreme range penalties by one die.
Use aim actions with trick shots.
L2: -2 restriction - may only use the attack if the target is unaware of you. Echos of shadow hand anyone?
+1 advantage - the attack gains the tearing property. So it does a minimum of one wound if it penetrates armor.
L3: -1 restriction - make a perception roll as part of the attack roll.
+1 advantage - the attack gains the accurate property. that's the hunting rifle, long laz, and needler property that makes then sniper weapons. Full round aim gains an additional +0k1 and for every +10 that you hit by you get +1k1 damage. I don't recall off the top of my head if you have to aim in order to trigger the bonus damage or if it's just there.
L4: +1 advantage - you can make a stealth roll at -2k1 after the attack. This can get weird if you're doing it at point blank with a shotgun while they're facing you. You'd need a shrub to hide behind or something anyways.
Bonus - get +1k0 to hit someone with ranged attacks if you missed them last turn.
L5: Bonus - For each full round you spend studying the target, for up to three rounds, you get +1k0 damage. What, like, permanently? Next shot? Plus this isn't a trick shot, it's a character ability. So, grenades and melee too?

Tin star gun kata.
L1: +2 initative. Look up there at the level 5 silent scope ability... That bit that says 'bonus'? that's me classifying stuff. By the book this initative and that damage boost are the same sort of thing.
Use trick shots with readied actions. Just like the sword school one, the readied action can't be a trick shot. Although if you can cross trick shots and maneuvers then I suppose "RAW" (as hilarious as that concept is in this game) you could ready a maneuver. You'd need to qualify the weapon and/or attack as both ranged and melee, but there's options for that.
L2: -1 restriction - you can only use the attack if you've lost half or more of your hit points.
+1 advantage - Quote: "The dice for this attack explode on +9." Attack, damage, associated skill rolls... Everything?
L3: -1 restriction - roll scrutiny as part of the attack roll.
+1 advantage - the attack ignores penalties from environmental effects, effects from damage, and having allies in melee withthe target. Cover (not a penalty, except maybe it can be)? The crits that blew off your hands and melted your eyes (definitely a damage effect)? Concealment (and to what extent, "I think he's in that room somewhere!")? I mean, smoke, rain, shaking, pain, fatigue, dazzled, those are all ok by me. Well actually dazzled isn't usually from damage. Does being hit with a webber count as part of the environment? Unsure.
L4: Bonus - reload any gun as a free action. Nice. This is good.
Bonus bonus -Again!? Choose a 'worthy foe' (no actual limits on worthy-ness) per combat and get +2k0 to attack them. If you attack anyone lese of any of your allies attack the foe you lose the bonus. Again, as a character ability... you verbially attack people in social combat. Actually I think I'd be ok with that.
L5: +4 advantage - Quote: "Add your dexterity as unkept dice with this attack." Well if you aren't keeping them then they don't matter do they!? Fast errata -> "Add your dexterity as rolled dice on the attack and damage of this attack." Because I think it's be nice to know what you're adding those dice to.

Dude. You had a good framework with the sword schools. Several of these are just outright messes, and some are pure power creep. I can understand the lack of deep play-testing but... elemental gearbolt level 3... ignores armor and resilience.

<Sigh> Ok, ok. After the read through I'll open an errata thread for the magic schools, sword schools, and gun kata. I'll even translate my java language dice roller into html and javascript so it will be a web page that anyone can download use in their browser.

In fact, quickie preview of intended gun kata errata: Clay pigeon L1: pistols and called shots. Crisis zone L1: burst capable weapons and the full auto attack, maybe suppressing fire too. Elemental gearbolt L1: primitive weapons and multi-attack actions. Point blank L1: basic typed (not pistol, not heavy) guns, overwatch & delayed actions (hrm, the actions on this and crisis zone are making more sense now, unsure). Silent scope L1: accurate weapons and aim actions. Tin star L1: exotic & ordinary weapons, readied actions.