From your screenshot of your media pool, it is easy to see why you are getting the Mount Requests
All of the media is Protected, that is, it all has dates on it. In order for media in the pool to be able to be used for Backup or Object Copy, it has to protected either
None
Expired
Last Media Used
Data Protector will not append to a media just because there is space left on it, except for the last media used by a previous operation. In this case you need to either format media into this pool, use 'Move Media' to move unprotected media into this pool, or Recycle some of the media that is close to the Expiration date
I don't know when this screenshot was taken, but all the media is passed its expiration date. If the Media is not moving to Expired status, you probably need to open a new case with DP support, but first, I would right-click on media past its expiration date, and click Recycle, which simply removes protection of all sessions on that media, enabling it to be reused
Do some backups, watch the expiration date and see it it goes to 'Expired' on that date
I can't comment on your Media Pool's Properties, but, if you are in a position to do so, you may want to consider using Free Pool