I have played through a significant amount of Adventure mode, I've racked up over 6500 points in online tournaments, and I still have a bunch of question marks on the character screen that I don't know what I can do about. How do I unlock characters in this game?
When you move your cursor over those question marks, the unlock condition will be displayed where the character normally would.
The three question marks require that you participate in an online tournament held in:
- July 2018
- August 2018
- September 2018
If you don't participate in those tournaments, the character will be unlocked the following month. By October 2018, you should've unlocked all character even without participating in any tournaments.
 Source: Mario Tennis Aces News on Nintendo Switch.