[RPG] Does an Incantatrix learn new spells per level

RAW: Ambiguous

The rules are not clear on what, exactly, constitutes an “arcane spellcasting class” or a “divine spellcasting class,” probably because initially it was obvious. By default, assassins, bards, sorcerers, and wizards were the arcane spellcasting classes, blackguards, clerics, druids, and paladins were the divine spellcasting classes. There was no ambiguity: the former are the classes that cast arcane spells, and the latter are the classes that cast divine spells. Easy.

Then they printed things like Alternate Source Spell, Rainbow Servant, Sha’ir, and Southern Magician, which introduced ambiguity that hadn’t existed before. In these cases, you have spell slots from one class being used for either arcane or divine spells.

Does this new feature suddenly make the class into an “arcane spellcasting class” or “divine spellcasting class” where it wasn’t before? There hadn’t ever been a strict definition before, and they didn’t print one at this point, either. Some of these effects seem to try to include wording that prevents this kind of thing, but much of those rules are also unclear. For instance, consider this from Southern Magician: “The actual source of the spell's power doesn't change,” which Customer Service interpreted as preventing entry to mystic theurge. But it doesn’t really say that, does it? It says something about power source, which is unclear.

Unfortunately, there’s no direct, rules-as-written, “as it says on page xyz of Complete Shenanigans” kind of answer to this question.

Recommendation: Never

RAW is ambiguous, but what’s going to work well in-game is not: never, under any circumstances, should one be allowed to advance wizard spellcasting faster than the wizard does. That should never, ever happen in any game, and if you’re going to allow it you might as well allow Pun-pun.

Allowing these sorts of tricks to qualify for mystic theurge, and other prestige classes and feats that require one type of spellcasting or the other, is pretty clearly legal, RAW, and also usually far less troublesome. The only exception I’d be likely to make is the dweormerkeeper from Complete Divine’s web enhancement, but then I’d probably just ban that class outright.

Even allowing a divine-only prestige class to progress wizard spellcasting is almost-always not a problem. It’s the double-progression that should never, ever happen.

Yes, they stack like the rule you cite says, if the specific class says they do. This is an example of exception-based design - the general rule is "only the one class counts" but then the specific rules in the other classes can say "but I do."

Not all prestige classes are alike so you should carefully read their Spellcasting benefit. In this case, Arcane Trickster says "I stack."

But classes that do not say that phrase, like Wizard and Sorcerer, do not stack. In your second example, Loremaster's spellcasting is worded like Arcane Trickster (as if she had gained a level in a spellcasting class she belonged to...), and you would need to decide whether you want it to stack onto your 5th level wizard spellcasting or your completely separate 3rd level sorcerer spellcasting. Assuming the former, you'd cast your spells from wizard slots at level 8 and your ones from your sorcerer slots at level 3.

It's kinda obvious why this is, the core idea behind prestige class design is "continue what you were doing, down a slightly weirder path" and therefore completely penalizing a spellcaster by e.g. halving their spellcaster abilities would be undesirable (even at that, many don't add a spellcasting level at every level and have one or two "penalty" levels.