The first formula is false when P is true, so it can't be proved. Concerning the third formula, either premise ~P v Q or ~R v S is enough. You can get them by conjunction elimination. The conclusion follows just by disjunction elimination (considering whether ~P or Q holds) and then disjunction introduction. The second derivation is slightly more difficult. It requires either the law of excluded middle (easier) or double-negation elimination (harder).