Time Machine is a very useful utility but for a case like this simply copying the contents of your 'old' drive to a new one is probably simpler.
"It is so rare to me. I've been thinking about a hacker. "
The reason I keep mentioning third party software is that if something, or someone, had reformatted your drive as NTFS there'd be no data on it now.
The fact that the data is still there suggests the drive was always NTFS,
and since MacOS can't natively write to NTFS that suggests to me that you've got some third party software for NTFS writing.
Are you sure you don't have some software like ntfs-3g, mounty, paragon, or sysgeeker, which has stopped working for whatever reason?
"Ok, could I back up just copying directly from drive to drive? (I just did it from the ext drive to a new folder in my Mac)."
Yes, absolutely. If there's enough room to do so then that's fine.
Move the entire contents of the drive either into a new folder on your mac, or on another drive,
then I'd recommend ejecting the source drive then double checking the contents of your newly made backup,
just to make sure everything is present and correct.
I can't stress that enough - Please be 100% certain that your backup is complete and taking up the amount of space that it should.
Double-check the size of the folder you've backed everything up to, to confirm it's the same as the used-space of your source drive.
If you're happy that everything's good, you can then format that problem-drive for MacOS, then put all your stuff back on it.
"Last, any suggestion about a good new drive for Pro Tools?"
I'm not really sure, to be honest.
You need a new one for a specific reason?