Military Advisor Response: After Military Advisor is wounded, pay 2 to choose and wound a character with skills lower then the Military Advisor.

If I lose a combat struggle, can I place a wound on Military Advisor and wound any character? Would I wait until the end of the icon struggles for it to trigger? How long do you have for a response to be able to trigger?

Unless the action is a Disrupt: or a passive effect, you have to wait until all the story cards that will resolve in that story phase have resolved. Then the response windows open up for all the things that happened in the resolution of all those stories.

So, if the Military Advisor is at story A, and some other stuff is at story B and nothing is at story C. Story A and B will resolve (in whatever order the active player chooses), story C will not resolve, and then you can use M.A.'s ability if appropriate.