Q: Does the data associated with an athlete stay with the athlete if I were to move them from one team to another?
A: Yes.
Q: If I were to place an athlete in my patient group (multi-sport) and once they are back to full activity and I want to move them to his/her respective team (swimming)
A: That should be fine. Planned and reported training data is linked to the athlete.
Q: If I assign a patient to a team with “swimming” as sport and then later move him/her to a different team (not subgroup), also “swimming” with the same activity list names, will the historical data move to the new team and show up in the new team reports and graphs?
A: Activities are stored by owner id and sport. If the sport doesn't change, then the activities should be the same. (If the sport does change then you may end up with activities for the athlete that don't match the new sport.)