Here are the answers:
Firstly, at any point, do the stored procedures change, get added or removed at any point?
If you are not performing an upgrade, the stored procedures do not change. They are placed when the database is created, and remain the same after that. I am not sure how you will corrupt the stored procedures, but if you restore them with such from the same version, there will be no problems at all.
Secondly, if I want to synchronize data between two existing Sitefinity
projects, will there be any differences in the stored procedures?
If two or more projects are connected to the same database, then these projects should use the same version of the CMS. Otherwise, on each operation with the database, it will be upgraded/downgraded in order to satisfy the schema version, required by the application. This might cause a lot of issues, when several users in several projects are working at the same time.
Thirdly, are there any differences in the stored procedures for Sitefinity 3.5 and 3.6?
There are differences. We have added a few more properties to pages and other stuff, that requires the procedures to be changed too. I am not able to provide you the exact changes now, because we use ORM which automatically handles the classes and stored procedures.
Let me know if I could be of further help.
the Telerik team