Can the system photo library be on a connected hard drive?

Drag it over will make a copy on the external drive. When that's completed hold down the option key while starting Photos and choose the library on the external. When you're sure the copy has gone well then you can delete the one on the internal.

Remember tho: you still need to abck up the library on the external to some other hardware.

One more question, is there a way to have the photos just on the iCloud Photo Library and not on the computer? This way my son can access all his photos from his iPhone using iCloud Photo Library. And when he wants he can download what he wants to a computer.

You can delete your local Photos Library and only use the web interface at www.icloud.com , but he web interface is much less versatile than using the Photos.app on a computer. To use the Photos.app on a Mac, you need a local copy of the iCloud Photos Library.

And with a local copy of your iCloud Photo Library it is much easier to backup your Photos. Making a backup of your library using the web interface is a lot of work and error prone, as we can only download thousand photos at a time.

Well this iCloud Photos is driving me crazy. I dragged the system photo library to the external hard drive and when it was finished I tried opening it to see if it was completed but I got a message so I clicked out. Then I moved the original to the trash and then opened the new one on the external hard drive, went to preferences and made it the system library. In the cloud there are around 14k of photos and some videos but when I open the system photos it still says 4,297 photos, 252 videos uploading 2,749 items.

Well this iCloud Photos is driving me crazy. I dragged the system photo library to the external hard drive and when it was finished I tried opening it to see if it was completed but I got a message so I clicked out. Then I moved the original to the trash and then opened the new one on the external hard drive, went to preferences and made it the system library. In the cloud there are around 14k of photos and some videos but when I open the system photos it still says 4,297 photos, 252 videos uploading 2,749 items.

I dragged the system photo library to the external hard drive and when it was finished I tried opening it to see if it was completed but I got a message so I clicked out.

What was the message and what does "clicked out" mean?

I'm no expert on iCloud. I personally use Lightroom CC for sharing across devices. It's more powerful but equally, less complex and more reliable in my experience. Mind you it's not free, of course. Other apps in the space include Mylio, which I also found very powerful and reliable.

Yes, as long as it's a direct connection (for instance USB or Thunderbolt) but not a Networked connection such as a NAS, and as long as the drive is formatted Mac OS Extended (Journaled) or apfs

Great thanks