now for triangular duel.
let's consider the first part of the problem:
i will start with the case that both A and B shoot into the sky. by assumption (1), C will shoot, and he will shoot B. this is because by (2), he will be the only one shooting till he kills someone. of course he would like to face A in the two-person-duel instead of B, as summarized in the following table:
(columns are A, B, C's action, their probability of winning, X means not preferable)
A B C P(A) P(B) P(C)