Sounds like you're off to a good start.

A couple of things you can do:

Right-click a database in SSMS (Management Studio), then Report -> Standard Reports -> Backup and Restore Events. That'll give you the backup/restore history of a particular database.

Get familiar with the system tables in database msdb. It's under Sytem Database in SSMS. The ones you want (for this subject) all start with "backup". They'll look cryptic at first, but once you read up on them, they'll tell you everything about backup history: where the backup files are going, when/if the databases are being backed up, what types of backups, etc. There are lots of good scripts available online for querying details out of these tables.

Get familiar with testing Restore on the backups. Always remember, you don't need a "backup plan", you need a "restore plan". Backups are useless if they can't be restored effectively and rapidly.