How to prove an implication within an if and only if Suppose you need to prove that $A\iff (B\implies C)$.
The two ways to prove this are:

(1a): Suppose $A$ and $B$ are true. Prove that $C$ is true.
(1b): Suppose $B$ and $C$ are true. Prove that $A$ is true.

(2a): Suppose $A$ and $B$ are true. Prove that $C$ is true.
(2B): Suppose $A$ is not true and B is true, prove that $C$ cannot be true.

Are these ways correct? I always get confused what you can assume and what you have to prove when there's multiple implications and such in one statement.

It helps to call $D$ the statement $B\implies C$. One has to prove $A\iff D$. So we need to show that $A$ implies $D$, and $D$ implies $A$. This means again, that, assuming $A$ it must follow $C$ if we assume $B$, and conversely, that whenever $C$ follows from $B$, then $A$ follows. Now check your $4$ statements according to this reasoning.
