I think they are all grammatically acceptable. But I would say (just to make things sounds more natural):
(a) Le chanteur, étant très aimé de/par ses fans, va chanter au concert demain.
(b) Le chanteur, très aimé de/par ses fans, va chanter au concert demain.
(c) Étant très aimé de/par ses fans, le chanteur va chanter au concert demain.
(d) Très aimé de/par ses fans, le chanteur va chanter au concert demain.
But the meaning changes quite a bit. Originally, we were just adding a precision about the singer with "qui…": that singer happens to be loved by his fans. In a,b,c,d though, we are now saying that the reason he is going to sing tomorrow is that he is loved by his fans. That was not present at all in the original "qui…". We have not just replaced the relative clause, but also changed the meaning!
So I would say that you cannot really replace the relative clause in this way while preserving the meaning, at least not in this case.
Note: (b) and (d) could IMHO go both ways: they could be understood to have the exact same meaning as the original sentence with the relative, or to introduce causation. The other 2, in my opinion, would normally be understood to introduce causation quite strongly.