1) yes correct 2) different meaning - negatively got between either physically or figuratively 3) yes correct

1) she acted as a go-between for me and him - ok 2) she got between me and him - She stood in the middle, literally or figuratively, as in disruptively 3) she acted as a go-between between me and him. -ok None incorrect, they just don't all mean the same thing.

Not incorrect but awkward. More natural would be “She was our go-between.” “She was the go-between in my /dealings/discussions/negotiations with him.”

They are good but they are differents in meaning

The answerers are correct about the difference in meaning in 2. However English speakers tend to put the other person first in sentences like this. So 'him and me' sounds more natural than 'me and him'