For the record, I'm fine with glossing over terms like "50% health" which, if they were to be like officially published or such, would need to be cleaned up. Everyone here knows what you mean, except me, and only when listed.
* = I think there's another game ability with this name.
Blaze of Glory - While the owner has no choice about whether or not to activate the trait, it's not as big of a downside as it seems at first. Not every enemy uses weapons. And "double ability" is a pretty hefty bonus, especially when both attack and damage rolls. It also heavily favors characters with multiple attacks.
I'm also worried about players taking this, and then taking very high defenses -- allowing themselves to get scratched below half, then immediately heal and get a very strong combat bonus. By contrast, without high defenses and/or when facing weapon-using enemies, this could get activated and then immediately kill the owner. That's too big of a gap of the application for me to approve.
Recommendation: Tone down both aspects of the trait. Add the same amount of damage, +prof, to the first hit dealt and the first hit taken each round. This is far weaker than the original.
Bloody Mess - There is no real benefit to this trait, and the downside (destroying the body) can be significant -- no meat from a hunted animal, unable to claim a bounty from a recognizable corpse, and as written the worst unable to knock an enemy unconscious. When used on a PC, this will also murder them -- and that's unacceptable. You wanted these to be a slight benefit, I can't think of a way this would ever be any benefit. Also the ability is always on, which can only reasonably be the result of magic or psionics.
Recommendation: After landing an attack intended to do lethal damage, the player rolls a 1d6. If the result exactly equals the target's remaining hit points, the trait goes off, killing the target. The DM may choose to allow a Constitution saving throw DC = damage done, or block it entirely for large or important targets.
Bruiser - As mentioned before, the penalty seems excessive.
Recommendation: If you're going to have both penalties, +2 to Str (max 20) seems more in line. Alternatively, replace the Dex penalty with a lighter penalty, such as Init rolls.
Built to Destroy
Recommendation: A "broken" weapon is improvised rather than 1 damage. I also see no reason it can't be repaired like any other broken weapon, requiring a craftsman and paying a fee.
Bullied - I actually like this one where it is.
Claustrophobic - The bonus and penalty are both so light I can't see this as a problem. But you need to add Agorophoic with the locations swapped.
Early Bird - Um...did you get the times backwards? Also, most adventures seem to take place at daytime, making this far stronger than Night Person.
Recommendation: Make them both +1/-1.
Edge of Death - This feels balanced, but is really risky. Don't expect anyone to take it.
Recommendation: To make it a little less risky, instead of dying on two failures, -2 to all death saving throws. Unfortunately this kind of dulls the edge, making it less likely to help.
Fast Metabolism - "Increased by 1.5 as much" means you heal double-and-a-half. I don't think you meant that? Also, even +50% feels a little strong, since most PCs will encounter healing far more than poison.
Recommendation: Replace the healing bonus with "if you don't like the healing amount rolled, you can roll again but must take the second effect". That caps the maximum effect while still offering a useful effect.
Fast Aim - -3 feels excessive, especially at low level. It's effectively equal to Disadvantage, the average result of lowest of 2d20 is 7.175 which means you're causing the effect of Disadvantage on the first attack, while only one-in-five letting them negate that by taking a bonus shot. Mathematically, this is a loss of damage more often than a bonus.
Recommendation: Changing -3 to -2 is a very slight increase overall to ranged damage. I also recommend you spell out that even weapons with Loading are affected.
I also like what you did later and, rather than have the player roll an extra die every round they fire, have the effect kick in if the natural die roll is (your choice of four numbers that aren't 1 or 20).
*Finesse - This is also mathematically a loss under a lot of circumstances. Example: you are using a 2d6 weapon. On a crit, you do +7 damage. You add a +5% chance of this, so this is +0.35 damage per swing. However, by sacrificing your ability modifier which is almost certainly +1 or higher, the damage you lose on most attacks more than covers the spike you can get from a lucky 19. Honestly, "Crits on a 19" is not that strong of a bonus overall, so the penalty needs to be much weaker than you're using.
Recommendation: To even it out, I recommend -1 to damage rolls if you hit by less than four.
Four Eyes - Any player who takes this will conveniently forget that they're wearing fragile glass on thin wire on the most vital target on their body, and their spectacles will become invulnerable through sheer forgetfulness.
Recommendation: Make spectacles a real issue, similar to how they were in Fallout 3 by limiting your helmet choice. If worn with Medium or Heavy armor and worn under a helmet, they just flat-out don't work. If worn instead of a helmet, creatures with Intelligence 13+ will automatically go for the face, getting +2 to attack rolls (MUCH simpler than any Called Shot rules I have seen) and a critical hit breaks the spectacles.
Gifted - I actually like this one where it is. Just don't let the PC's "save/reload the game" until their primary stat comes up.
"Can we go to the dungeon today?"
(die clatters) "No."
"Can we go to the dungeon today?"
(die clatters) "No."
"Can we go to the dungeon today?"
(die clatters) "Okay we're good."
Glutton - No dwarf would ever take this.
Recommendation: Prohibit dwarves from taking this.
Good Natured - Bonuses to skills are, generally speaking, weak enough that I think this is probably okay. A support character could really go for it, and even support characters attack when things are going well.
Heavy Handed - Okay we've talked about this a bit before. Because crits happen so rarely the benefit is now much stronger than the loss. This is a must-have for dual wielders who roll small dice anyhow, making the penalty even weaker. However unlike Finesse you're only adding +1, so this is closer to balanced.
Recommendation: The +1 to damage applies only when you hit by four or more, cutting down the effective bonus.
Hoarder - The penalty means nothing since the PC will just fill their pockets with Minecraft dirt until they're at the listed weight. Then they'll drop the dirt and replace it with treasure as they find it.
Recommendation: Simply cut off the benefit if they take items with no inherent use or value. If they, say, carry bags of hammers and drop the hammers, at least you know they're losing money.
Hot Blooded - -3 to AC is crippling. Nobobdy will take this.
Recommendation: Make it -1 to AC, which is plenty, restrict the action to either a single attack or movement, and the player can use it on their first round after rolling Initiative.
Illiterate - It makes a lot of sense to forfeit reading ability for some other skill. But a saving throw prof seems a bit much.
Recommendation: Swap out "ability to read" with another skill from their class or background. Later, if they gain the ability to learn a skill, they can learn to read instead ending this trait.
Jinxed - This feels like it would benefit melee more than ranged since more monsters with melee attack rolls than ranged attack rolls. But it feels like this one's also balanced. Just a heads up: it will slow combat down.
Loose Cannon - There's a lot of crossover here with Fast Aim. A lot of thrown weapons have a pretty low normal range, and cutting in that in half, probably to 10 or 15 feet, makes them really hard to use.
Recommendation: Either merge this with Fast Aim, or make the game effects the same.
Recommendation: See Early Bird.
One-Hander - I mentioned this before, too.
Recommendation: I'd tone it down. +1 to weapon attacks if using a single weapon in one hand and nothing in the other hand, -1 if using any other weapon and/or shield combination.
Optional: Melee only.
Paranoid - It's balanced, but doesn't fit the name. I'd imagine paranoid people being jumpy, not sluggish. -2 to Insight would be balanced, but the bonus/penalty would both be pretty weak.
Recommendation: Advantage on saving throws against being Charmed, disadvantage on saving throws against being Frightened.
Romantic Appeal - There's soooo many more creatures that "aren't attracted to you" making the penalty just not worth it. The wording on this one could be cleared up involving "approrpriate race/gender" but that'd be clumsy and, um, too many ways it can be badly done and offensive.
Recommendation: Make the bonus +2, the penalty -1, and the DM can make either +0 when it just doesn't make sense (such as lizard man negotiating with gargoyle)
School Specialist - As written, this could be very dangerous. A specialist could simply take a bunch of spells from one school and nearly nothing else, doing massive piles of damage. Actually, at first/second level, the spellcaster has no choice at all.
Recommendation: Don't use this one. Wizards seem to have it under control and I don't see other classes fitting the theme.
*Skilled - Okay the problems here are multiple. There's a Feat called Skilled and this feels awfully similar. However, most players would not agree to cap their primary stat at 18 (making the penalty too strong) unless they knew they'd never reach high level (in which case there's no penalty at all).
Recommendation: Rework the penalty. The player cannot take +2 to the same ability score when taking Ability Score improvement.
Small Frame - In any game with encumberance, cutting it in half is devastating.
Recommendation: For only +1 Dex and the swim/climb penalty, I'd go with a much milder reduction, such as -25% or maybe even -25.
Truth Teller - This one seems balanced to me.
Wild World - Obviously the DM should get final say.