You can certainly run backups of the Primary node of the mirror and do them online just like a server that is not being mirrored. As far as the backups are concerned they do not care if you are mirroring. I would recommend backing your DBs up and do not rely on the mirror as your backup. As far as checking if Mirroring is working MS has a tool that will do this for you. Just goto your SQL Server Management Studio and connect to the instance. Once connected expand the databases tab. Once that opens you should see the name of the miroed DB and it should say Principal and whether or not it is synchronized or disconnected. Then right click on the Database and go to tasks then to Launch Database Mirroring Monitor. This will have you register the server and will show you the Mirror and show you the data transfer between the servers.

You can certainly run backups of the Primary node of the mirror and do them online just like a server that is not being mirrored. As far as the backups are concerned they do not care if you are mirroring. I would recommend backing your DBs up and do not rely on the mirror as your backup. As far as checking if Mirroring is working MS has a tool that will do this for you. Just goto your SQL Server Management Studio and connect to the instance. Once connected expand the databases tab. Once that opens you should see the name of the miroed DB and it should say Principal and whether or not it is synchronized or disconnected. Then right click on the Database and go to tasks then to Launch Database Mirroring Monitor. This will have you register the server and will show you the Mirror and show you the data transfer between the servers.