- Yes
- Yes if the table is using the MyISAM (default) engine. Not if it’s using InnoDB.
- Probably not, and if there is, you just need to execute mysql_upgrade to fix them
To avoid getting databases in a inconsistent state, you can either shutdown MySQL or use LOCK TABLES and then FLUSH TABLES before the backup. The second solution is a little better because the MySQL server will remain available during the backup (albeit read only).