Assuming you have persistence turned on for every module:

1. Theoretically nothing - the existing profiles are restored and OPCOM will pick up from where it left off.

2. Adding new Placement modules will spawn new profiles where none existed before. If you remove a Mil Placement altogether, it will (I think) probably break the persistence for those objectives. At least, they may be restored but OPCOM will have nothing to refer to as it's not synced to a Placement module. Not entirely sure how game breaking this could be!

3. I don't think that's persisted (yet), so should change as you require. This may be different in upcoming releases of Asymmetric Warfare though.