When you connect to the same source and destination as a previous migration, the mapping selections you last saved will be restored. This occurs even when starting a new migration.
Users, Permission Levels, and Site Templates are handled at the site collection level, so when the source and destination site collection are the same, the mappings are maintained through all sessions.
Property mappings and Content Type mappings are associated to a specific list, so these are maintained when you connect to the same lists as a previous session.
If you restore a migration using Recent Sessions or Return to this session from the Migration Report, your mappings wills still be the last mappings saved when you were connected to that source and destination, and not necessarily the mappings you used for the original migration session.
If you restore a migration using Recent Sessions or Return to this session from the Migration Report, Sharegate will restore the copy options that you had previously saved for that session
If your migration is a Copy Structure, changing the source or destination of a restored session will not affect the copy options. However, if your migration is a Copy Content, changing either the source or destination from a restored sessions will reset the copy options to the default values (but you can always access your saved templates from the template dropdown).
Title and URL are always reset if you change the target in the source or destination.