What happen with an outpost wich its destroyed by the martyr, it still fulfills it function or its useless? Also what happen if another person capture the outpost after

It's useless. No function, and it doesn't count as an outpost for the purposes of Neptunium production either. It only gives vision to the player who controls it.

And please refer to the FAQ document on top of the Questions thread before opening new topics, since its most likely you will find your answer in it.