Yes. May be a bug, but all influence effects that are side effects of states apply even if the influence is otherwise locked in a conflict. (This includes expansion tax)So Infrastructure Failure affects faction's influence in a war state?
Preventing a second war, same as you'd try to prevent the first, but while the IF is going on you've got a bit more against you.
Murder of the opposing ships may [1] well give them Infrastructure Failure / Blight / Drought / Terrorism which will directly drain their influence and even the odds a bit.
[1] The exact causes of these states aren't known, but generalised murder and mayhem does seem to give Infrastructure Failure or Terrorism fairly often.