The Killing of a Sacred Deer

If Martin had super human powers then why didn't he save his father's life to begin with ?

Who's to say Martin wasn't his father. Martin may not have existed until his father died and then he was manifested to test Steven.

But then wouldn't the Mother have known that this was not her son ?

Did anybody say he had super powers or are you just saying it because of things he did in the movie, it's all a metaphor.. in case you don't get it there's a moment in the film where Martin explains it's all a metaphor , he's not spider man mate.

If he is responsible for super human things , making everyone sick, then it must mean that he has super human powers. Or did he just poison everyone ?

Neither

Well then what was happening to the family to explain their condition ?

To put it simply, a magic curse. The question of how Martin manages to do these things is completely irrelevant - what matters is how Steven and his family deal with such a nightmarish situation.