The Erudite Spell to Power variant allows you to "attempt to convert an arcane spell into a power you can add to your repertoire". The description then repeatedly refers to the resulting spell/power as a spell, but follows that up by saying "Because the spells are now effectively psionic powers, they are no longer affected by metamagic feats."
So, the StP Erudite pretty clearly qualifies for the classes that require the ability to cast specific spells, just like an invoker with the right invocations does. ("[S]pell-like abilities that generate the relevant effect meet the requirements for specific spell knowledge." CAr, page 72). The CtP Erudite, by the official rules is doing pretty much the same thing. It's generating the relevant effect of a spell through different means (in this case as a power/psi-like ability, rather than a spell-like ability). Best reading of the rules currently available is that those requirements translate to "can generate X effect". On the other side, they do not have a caster level, and do not qualify for classes that require one. Like the invoker classes, they would also not qualify as either prepared or spontaneous casters.
Beyond that, it gets a bit messy. The text repeatedly refers to what you are doing as casting spells as psionic powers. RAW, then you are able to cast spells, and those spells have levels. This would qualify for prestige classes that have "cast spells of nth level" requirements. Most of those prestige classes wouldn't be worth it, though. It would be pushing things to claim that the Erudite class qualified as a spellcasting class that could be advanced by such classes, and even if it did, improving "spells per day, caster level, and spells known" does the Erudite no good. Also, the Erudite is effectively a full caster chassis, which means that any prestige class that doesn't advance psionic ability is a waste. The only real option to try to take advantage of this appears to be psi/arcane theurge classes (Cerebremancer or Mind Mage), using the erudite to qualify for both sides and dipping one level into a caster or invoker class to make use of the spellcaster advancement. That's rather clearly not RAI for theurge classes, though.
This DM would say that it makes more sense to just treat them as pure psionic powers rather than weird spell/power hybrid things. That's a DM ruling, however, rather than RAW.
