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Reading over the Warmage, there wouldn't be anything from restricting them from doing this. Taking the feat Extra Spell would allow a warmage access to additional spells beyond the evocation school by the looks of it. Yikes, it would take feat expenditure, but now all of those important defensive spells are open to the warmage.
No. Extra Spell allows you to learn an additional spell from your spell list. A Warmage has full access to his spell list anyway (like a cleric/druid), so he does not benefit from the feat at all.
Exactly. You cannot learn spells, which are not on your class list, unless it is specifically noted (as with the Arcane Disciple feat). A feat that does this would also have to add the spell to the class list. Extra Spell does not do that.
I don't have my book with me right now so sorry if I'm wrong but dosen't the feat state that it allow you to learn a spell you wouldn't normally have access to ?
And that part only means, that a wizard would only have a reason to pick up this feat, if he or she was somehow prevented from learning a specific spell (i.e. free level up spells already spent on other spells, no scroll or teacher available and no time for research - aka no access to the spell).
It does not mean, that you suddenly gain access to spells that are not on your spell list. The feat only allows you to learn an additional spell, not increase the base of your knowledge by adding a completely new spell to your class spell list.
Well, there is still Spell Penetration and Greater Spell Penetration, and magic items, followers, allies, party members, opponent's without spell resistance and more importantly spells, which do not allow spell resistance (even some of those in the Warmage spell list).