To start, could you clarify the syntactic conventions? It is usually assumed that implication associates to the right, i.e., 段 /\ p -> q -> 殆 is 段 /\ p -> (q -> 殆). I also assume that /\ binds stronger than \/, i.e., p \/ q /\ 殆 -> q is p \/ (q /\ 殆) -> q.

Yes, or some modification of the truth table method.

If you know how to construct truth tables, then you should be able to do this for these formulas. Otherwise, what exactly is your question about truth tables?

It is sometimes easier to try to find a falsifying assignment (valuation, interpretation). For example, if 段 /\ p -> (q -> 殆) is false, then 段 /\ p is true and (q -> 殆) is false, which means that q is true and 殆 is false. From the last two facts, both p and q are true, but then 段 /\ p is not true. Since there is no falsifying assignment, the formula is a tautology.

There is a falsifying assignment for p \/ (q /\ 殆) -> q, but not for (p \/ q) /\ 殆 -> q.