Do I have to run an inventory job for each day or can I just let it go and have Backup Exec just think that that same tape is in there everyday?
Any time you swap a tape you should run an inventory for it to be displayed in Backup Exec. Although, if the Windows Removable Storage service is running that service may detect the tape has been inserted and initiate an inventory for that service and the information it retrieves should get passed to BE, but still you should run an inventory if you want the new tape label to be displayed in BE. BE will also run an inventory when a backup job starts; this happens because BE needs to know what tape is in the drive so it can check what the overwrite and append time periods are assigned to the media based on the media set to which the tape is assigned.
Does Backup Exec keep the media label description after you eject a tape and put it back in the drive and does it somehow recognize each tape you put in the drive so I can label each tape according to the day it is used?
Answer: BE maintains the media description and it is written to the BE database. BE will recognize the tape when you run an inventory on it and display the media information as stored on the tape and in the BE database.
You might just want to manually assign a label to the tapes and then write the same label name on the tapes paper label in the format of 'Monday', 'Tuesday', 'Wednesday', etc...with the last tape labeled "Weekend'.
I'm estimating the problem you are having with the job not wanting to write to the media you provide is due to the Media Overwrite Protection level. Try this: click Tools > Options > Media Management; place the bullet for "Media overwrite protection level" to None and remove the check mark for the item below it. By doing that it turns off media overwrite protection completely and then BE will overwrite any tape in the drive. The caveat on that is that you need to make sure you don't put the wrong tape in the drive because if you do then BE will overwrite the data you want to preserve.
If you have other feelings about what you want to do then the best thing is to read the BE Admin Guide section 6 Managing Media starting on page 257 .
The BE Admin Guide can be found at the link below.