1) Not quite. MyGM puts you in the shoes of a GM so it makes sense that you can only control one team. MyLeague allows you to control all 30 teams if you want; you certainly don't have to though. MyLeague with just one user team is possible.
2) Both modes will allow you to do that. Depending on how much you want to deal with player complaints and owner expectations, either one works. The biggest difference is that MyGM has you meeting with players, staff, other GMs, etc. to discuss anything from playing time to practice focus to who you should draft.
3) I don't do Player Lock but I believe it's possible in either mode. In MyGM, you obviously wouldn't "player lock" the cut-scene stuff though so you could find yourself as GM talking to the guy that you're locking onto. If you want the ability to lock on a player as he moves around the league, I think you'd have to go the MyLeague option.
I've played both and enjoy both. I really like the RPG elements of MyGM and did one season in that mode before switching over to MyLeague. I guess the nice part of MyLeague is that you can customize SO many things from how often trades/injuries happen to how the cap changes over time. If they took either one of the modes out, I think I'd be initially disappointed but the other one would work just fine for me. Also, with MyLeague, you could easily take control of another team if you get bored with one whereas in MyGM.
To figure things out for yourself, you could always just create a sample file in each mode and mess around a little to see how it works. Maybe create a file, check out the menu options, sim through a few weeks, check out a few other things, and then sim to the off-season and try that. I usually do that when the game first comes out so I can familiarize myself with the different interfaces and nuances before I jump into my "real" file.