(She is the best member on the team.) This is the correct way to say the sentence. You could also say. (She is the best player on the team) a person is said to be on a team or a part of a team. You will not here a native speaker in a team.

There isn't a difference here, and you could also use "member of the team". All of these are fine. However, saying someone is the "best member" is a little strange. It is like saying "she is the best at being a member". Probably you mean that whatever the team does, she is the best at, and while this is implied, it would be better to say what it is that she does well. "She is the best player on the team." That is, "she" plays (the sport or game) better than the other members of her team. "She is the best worker on the team." That is, "she" works better than the others.

Perhaps the usage here varies? To me, 'member in the team' is fine, and (as rcompass says) would be most common when referring to a work team. I would also use 'in' for a sports team, although I think that Americans tend to use 'on' more commonly in that situation.

In my opinion, 'on the team' means somebody is a player, but 'in the team' means somebody works for the team, for example a physic. I doubt the native speakers don't distinguish between them.

i can't tell you they different