1) You can "lock the door" - there is no limitation on the no. of schools. However, in general, only your 1st or 2nd choice in the list will consider your application again. It is not worth to waste your time to submit the application to too many schools.
2) You should submit the application for "locking the door" asap. Of course, you can send the profile later (after you register) - but the space is limited (only a few is available). If you are late, the space is filled up already.