1. Quoi = what (indirect object)
Don't use quoi in written French without a preposition, as quoi stands for indirect objects -- except in fixed expressions like quoi qu'il en soit (nevertheless).
Quoi only appears in questions as the second word, directly after the preposition. Typical prepositions are de, à, sur, sous, en, pour (in this case, both words are written together in pourquoi). For example: de quoi parles-tu ? (what are you talking about?); à quoi fais-tu allusion? (what are you referring to?)
Quoi is misused in the spoken French in a grammatically incorrect but sadly very common way as a substitute for que in non-inverted questions: tu fais quoi ? standing for que fais-tu ? (what are you doing?)