Overall I think you may have overshot power-wise...

Limit Break
Awesome idea, helps shore up some of those lower level spells for the blasters. Nothing wrong with it, though you may want to think about capping the increase at your archmage level.

High Arcana - Magic Mastery (Ex)
Spoiler
Show
An archmage is a master of magic, adding a +1 bonus per archmage level to the DC of all saving throws for spells that he casts that permit a saving throw. Any attempts by a non-archmage or an archmage of lesser level to dispel or counter the archmage's spells automatically fail. Any effect the archmage personally produces with magic is irreversible, except by the archmage himself. This prevents spells like break enchantment, disjunction, remove blindness, or remove curse from working.
This ability is doing way too much. +class level to DC is a little over the top as is. Adding to that the inability to counter, dispel, reverse, etc any of the archmage's spells makes it even more difficult for the DM to challenge the mage because there is no defense short of another archmage of equal or higher level.

Perhaps you could try making it 2 abilities, something like this:

Magic Mastery
Spoiler
Show
An archmage is a master of magic, adding a +1 bonus per archmage level to their caster level for the purpose of penetrating spell resistance, dispel checks made by them, and to the DC of any caster level check made to dispel or otherwise end any spell effect of the archmage. If the effect does not normally require a caster level check, it does when trying to break an archmage's spells. The DC for this check is 5+the archmage's caster level.
This way the archmage's effects are much tougher to break and can even give disjunction a hard time, BUT it isn't absolute. The DM can still check and challenge the mage.


Magecraft
Spoiler
Show
An archmage is exceptional at weaving more potency into their spells. The archmage may increase the spell level of any spell they cast by 1/2 their archmage level (rounded up) to a maximum of the highest level of spell they could normally cast. This effect is similar to heighten spell, but does not use a higher level spell slot.
So now the mage can up the power of most of their lower level spells without pushing beyond their normal highest DC and overpowering their strongest effects. It increases the potency and variety of effects they can bring against stronger opponents.


Anyway on to...
High magefire
Probably the most tame ability here. First you may want to clarify how metamagic is applied to it. Second clarify the damage type it deals (I'm assuming raw arcane damage and thus not subject to any resistances). Third, clarify if ranged touch, saving throw, auto-hit, etc.

Metamastery
Very powerful ability. Imagine the persist spells. I would recommend allowing it to be taken multiple times for 1 use each rather than scale with level.

Spell-like ability
Definitely too much. I would suggest reducing the number of uses to the archmage level at the very least and even that seems quite powerful when applied to the highest spell level.

So anyway yeah, good job with the update of the archmage. You came up with some great ideas for useful abilities, now just refine them and you'll be golden.