Yes, this sounds all right. There are several other ways to say it of course.He has a habit of getting into unneccesary fights.
"Taking up a fight" might be used in the context of continuing a dispute started by someone else. I wouldn't use it in your context.If not can I say that he takes up unneccesary fights?
Check your spelling of unnecessary Make sure the double letters are all in the right places.
Does it mean that the person fights a lot and that he takes up a lot of fight. I don't understand this part - it is not idiomatic English - could you explain it?