Send you a message [through] your most used app/profile without needing an [account] on that service
No, I don’t think so…
However, what you’re describing kind of sounds like a polycentric identity. Maybe check that out. Also, I believe ActivityPods aim to handle a little of what you’re describing, but I don’t know how much adoption it’s had.
You never need to go to a gym to get fit. It could help, for some people, but it is not a necessity by any means!
You don’t even need weights or equipment; calisthenics are valid.