I've considered the case of four shooters. I considered strategies in the sense of question 4, with the referee's order (1,2,3,4). What I discover is this:

1's dominant strategy: (4,3,2) in case there are four people and (3,2) (4,2) (4,3) in case there're 3

2's dominant strategy: (4,3,1) and (3,1) (4,1) (4,3)

4's dominant strategy: (3,2,1) and (2,1) (3,2) (3,1)

these 3 people behave normally: they just shoot the most accurate shooters first.

3's best strategy, however, turns out to be unexpected. To appreciate this, let p1=0.91, p2=0.92, p3=0.93, p4=0.94. In case of 4 people, what will 3 do? Now the effective order is (3,4,1,2). If 3 shoot 4 first, he has very high probability of success. But if 4 dies, the effective order becomes (1,2,3). From the above we know 1 and 2 will shoot 3 first, thus 3 puts himself in a very dangerous position. Actually, it is best for 3 to shoot 2 first! If 2 dies, the effective order becomes (4,1,3). Then 4 will shoot 3 first, but this threat is far less than the combined thread from 1 and 2. Furthermore, 1 wil first shoot 4 instead of 3 with high probability of success, increasing 3's chance of survival even more.