Upgrading and restoring hard drives in mid-2011 Mac Mini Server
To answer your questions as numbered:


Yes the computer should have seen both drives. Have you checked to make sure the drives are properly seated and the SATA cable plugged in properly?
I would always suggest doing a clean install of the OS and using Migration Assistant instead of Time Machine (you can do a Migration from a Time Machine backup) because anything that's currently associated with the UUID or anything else specific to the old HDDs may be weird when it recognizes the new drives as being different. Migration assistant fixes these problems and makes sure any app licenses transfer properly.
As I stated in my answer number 2, I would argue yes, with some changes.


If I were you, I would take the following steps:


I would try to figure out why my second HDD wasn't showing up. If necessary, I'd take the computer apart and replug its SATA cable.
Once I had both HDDs working, I'd format both of them to their final formats (likely HFS+).
I'd do a clean install of MacOS Sierra.
After setting up the computer, I would use spotlight to open the Migration Assistant app and migrate from that time machine backup.
Once the migration was complete, I would make time machine back up all of the data. This way, all of the new, migrated information has a backup.