i have... archmage is one of the better PrC's out there.
As for gaining new spells, your daily capacity for spells does not improve past 20th level unless you gain the Improved Spell Capacity feat from the Epic Level Handbook, although your caster level does increase normally, and new spells can be learned & recored into your spellbook.
High Arcana powers all have a trade off- you sacrifice a spell slot (each power causes you to lose one spell of a certain level) to gain use of a innate power.
For example, a archmage who selects Arcane Reach as his High Arcana power can now deliver all touch spells at a range of 30'. The trade off is that he permanently loses 1 7th level spell slot (that is, he now can memorize & cast 1 less 7th level spell that he should be able to at his level)
Hope that cleared it up for you