First-- iCloud does not back up your pictures. iCloud synchronizes your pictures. I have a backup in case I accidentally (or stupidly) delete a picture and later find I really wanted it-- I go to the backup and restore it. But with iCloud, if I delete a picture, it is deleted from iCloud, from my iPhone, and from my iPad-- it's gone from all of them. That's what synchronize means. That's why I have a backup.
Now, do you have "Optimize Storage" chosen, or rather "Download Originals" checked on each of your devices? If you have "Optimize" chosen on your Mac, then what you transferred to your external drive may not be full sized images-- you need to switch to "Download" since you now have the room. Then you need to make a backup of that library after it has download the full sized images.
On your iPad, once you turn off iCloud in Settings>Photos, the iPad is no longer connected to the other devices. Deleting a picture on the Mac won't delete it from the iPad. Taking a picture with the iPad camera won't send it to the Mac.
If you had "Optimize" chosen on your iPad, I would expect it to ask if you want to download the originals before disconnecting. If you don't, you will be left with the smaller versions. If you want more room, you can delete pictures.
Of course, if you leave the iPad connected to iCloud, you can choose "Optimize Storage," so then only smaller pictures would be kept on the iPad. But if you've already done that, and you still want more space, disconnecting and deleting pictures will give it to you.
Well, that sounded a little complicated-- let us know how it goes...