I believe based on your notes that I need to forget about moving the iPhoto library.... even though I have found in Apple support:
http://help.apple.com/iphoto/mac/9.5/#pht6d607c42
That document says.. and I quote.
You can move your entire iPhoto library to a different computer, a hard disk, or another location on your computer.
Note that none of those locations are network.
A different computer is not network.. a hard disk is a location on the same computer as is computer location.. they are saying the same thing.
Here is what apple says about networks.. which I referenced above.. and Bob referred to.
It's recommended that you store your iPhoto library on a locally mounted hard drive. Storing your iPhoto library on a network share can lead to poor performance, data corruption, or data loss.
These are not inconsistent.. you can move the library.. what you cannot do is use it from a network location.. it must be locally mounted.
And do you think the new Photos will change any of this (though presently I am still on 10.9.5)
This is what we don't know yet.. it does look like photos will be more network aware.. do you want to be on the bleeding edge and discover it fails??
You can use any drive you like locally for TM backups.. however if you plug that drive into the TC and make it a network drive then it will become super slow.. since the TC only has USB2 port. You also cannot use TM backups on a local drive and then move it to the network.. TM backs up differently in network cf local drives.
You must partition the drive. If you want to use the one and same drive for both backups and files, partition it before hand. if you mix the backups with actual data files on the same drive.. you have no backups if the drive fails.. You must have all files on at least 2 drives. For iphoto let me suggest more than 2.. since photos are irreplaceable and it is so easy for things to go wrong.. including fire, flood and theft. Make up a USB drive and park it with relatives.