The wizard in our party, got into this big argument (one could actually call it a tantrum) about if he is able to cast while paralyzed. He had this feat, sudden still spell, which works exactly like still spell, but does not need to be prepared with the slot. So I guess my question consists of two parts:
- Which feats must a character have in order to cast while paralyzed?
- Are you able to speak while paralyzed?
That part of the question came from the wizard's argument, that he had the still spell, so he did not need to use a somatic component, and the only problem was the verbal component of the spell. He said that no one can prevent you to speak while paralyzed.
D&D 3.5's definition of the paralyzed status reads (emphases mine)
So when paralyzed, you can't speak (referring to question #2), as that would be an action, and not a purely mental action. There is so corroborating evidence in the D&D Glossary on WotC's site which refers to the monster action Paralyze:
though one might consider the fact that it was explicitly added to mean that it differs from the paralyzed condition,
Now, for question #1: a spell can have Verbal, Somatic and Material components. Still Spell only eliminates the Somatic component. Adding Silent Spell will take care of Verbal, and Eschew Materials (for most standard materials)/Ignore Material Components (for the rest) for Material (apart from Focus or Divine Focus, which are much harder, if not impossible, to get rid of), as KRyan and Vereos noted in comments. However, this question still isn't addressed explicitly in the SRD. It is mentioned in the Official FAQ, though:
So if you accept the FAQ as RAW, and willing to accept the Expanded Psionics Handbook are RAW for spells, then these three feats would be enough to cast a spell while paralyzed, or any subset of them for spells without the relevant component.