Nobles character in blue is the best example or a grunt albeit her team isnt normally villainous.

To addrss some of your questions.

1. Stealing is a crime but you won't nessearly be robbing people by force. Granted that will be an option at certain points. Stealing can be as subtle as hacking a pc, or taking a pokemon when someones not looking. You will also be able to directly capture pokemon in the wild.
2. Grunts will have access to pokemon. With the ranks ups you will unlock new groups of pokemon. Before you ask it wont be all pokemon. Youll still need to capture or steal if you see another you want.
3. Be smart about crime! If you attempt to rob a store in the middle of the day theres a high chance youll get caught.
4. You can battle gym leaders. Since youll be mostly be stealth. No one will know you and the better you are about not being known the easier it will be to do whatever everyone else does with freedom. But like in many games to much bs can build up a reputation which is why i said characters could end up locked up.
4. Getting home should be a priority, however team Galactic will be more like a series of jobs where certain items will need to be stolen to help the bosses reach their objectives.
5. Your character can be a decent person, i think any character joining should know that this story is about crime. So if anyone at all joining said, my character could never do any of that. They wouldnt be allowed in this specific story. We have plat which can give them the straight and narrow path.
6. Like any gang recruiting kids, its all about making you feel part of a family and letting you be free to an extent. However just like a gang the punishments are tough.