Fact 1: Mike Grose was Roger's friend from Truro and he became the first Queen bass player. If I remember well, he also played with Smile (probably as a guest?)
Fact 2: John Grose was Roger's friend and they were both in (Johnny Quale &) The Reaction.
Question 1: Was Mike John's brother? Some sources say yes, some say no.
Question 2: Did Mike really play in all three bands - The Reaction, Smile and Queen?
Yes, correct on all three counts Martin. Mike was John(nies) younger brother.
However, his stints in Reaction and Smile were transcient. In football terms - he was in the squad, and very occasionally got a game as substitute, but he was never really in the team (if that makes sense). Partially because he never really was that great a bass player, but, was still a very handy person to have around.
I believe Mike still lives in the area, and is now the managing director of a haulage company. When Queen first began their concert career, it was Mike's company who initially transported their equipment.