Photo Library on Hard Drive won't open in Photos

You don't say if you are currently using iCloud Photos. If you are, then all the pictures in your Library are already at iCloud.com-- you should go there and check.

Photos has to be running with the Library in order for it to synchronize your Library with iCloud, so if it doesn't keep going long enough, then your only hope is to connect another drive to the Mac and drag the Photos Library to the new drive, as you've said.

When you open the newly moved Library in Photos, you may need to designate it as your System Library at Photos' Settings>General.

Beware: Using a Photos Library from an external drive on a mobile device like a MacAir, plugging and unplugging the drive while Photos does its background work, might cause problems-- the Mac may not want you to disconnect for some time. If you use iCloud Photos, there may be syncing issues. You might need to actually shut down the Mac before unplugging. I don't know that we've seen database corruption from this, but I'd be careful…

Apple's support document does not mention the case-sensitive flag. But it may cause problems for two reasons:

• By default the internal Macintosh HD will not be formatted case-sensitive. Copying libraries to a case-sensitive drive may result in broken paths.
• The system may not be able to find resources inside packages, like videos in a container format (Quicktime, AVI, HEIC) etc.

If the failing drive is not staying mounted long enough, you can try to copy the library in small steps by opening the package and copying one internal folder at a time, see: How to avoid the Error -36 when copying a Photos Library - Apple Community

1. The Cloud is a sharing service not a back up. Your best bet is to move the library to another HD. That HD shield be formatted Mac OS X Extended, Journaled or apfs
2. What format is your HD?

djmeuk wrote:

1. HD Format: Mac OS Extended (Case-sensitive, Journaled)

That should be Case-insensitive.

Yes you need it to back up that library.