Lets first with you last question: iPhone backups are saved in ~/Library/Application Support/MobileSync/Backup/ not in your iTunes Library.
Now regarding a setting up a new Mac.
I would be sure to have a good backup of your current system/
I would make a bootable backup with Carbon Copy Cloner or SuperDuper!
It would be interesting to boot such a backup on your current machine and see if the Movies are still reported in EB.
This might not tell anything decisive if they are still reported in EB, but if they are not then you now that your system is fine and you have, in essence, escaped some anomaly in the structure of your current boot disk.
If you have the storage I'd also have a Time Machine backup.
On getting a new Mac I would use Setup Assistant when you first boot it and if you have a time machine backup I'd use that as the source. See: Setting-up a new Mac from an old one, its Backups, or a PC
While you still have your old Mac, you can test the resulting migrated system to see if it is working OK.
If not then you can revert to manually copying your stuff.
That's what I'd do, but others would say take the "bare" system that comes with the new Mac and manually copy/install just wjhat you need and leave all the old, unused cruft on the old system/ This assumes of course that you no which is which.