A backup of the SQL database will include the schema, Management Agents, and even the rules extensions (they are stored as binary blobs in the database), but it can be handy to have just the Management Agents and Metaverse configuration saved and backed up separately. You do not need to stop the MIM Synchronization service before performing the backup, but you should verify no Management Agents are running because a running Management Agent means data is being processed.
The most common restore problem with the MIM Synchronization service database is a lost encryption key. If you need to restore the database without providing the encryption key, you will lose all MA connection settings and will have to reconfigure them. Re-entering service account passwords and clicking on Next a few times may seem a minor thing, but keep in mind that you will lose any initial passwords of users that are in the process of being provisioned. If you look at the pending exports...