would "who is your favorite player on the team?" be a better, more natural translation of what is intended here?

This is not how we say it in English. It should be: Who's your favorite player on the team? Reported.

Not "in the team", but "on the team".

In British English, most regions say "in the team" not "on the team" (which is considered American where I'm from).

explain why "on"?

Please, say, is "in the team" the right variant?

I think correctly is "in" no "on" the team