What formats are accepted?

Photos does not reject duplicates. It is just issuing a warning, if you try to import the same photo twice. It will give a warning that the photo is already in the library and ask you, if you want to import the duplicate nevertheless.

JEPGs are supported by Photos, also HEIC, TIFF, PNG, GIF.

Photos is warning about "Incompatible" photos for several reasons. It can even reject the a photo with the extension "JPEG", if the color sync profile of the image is not compatible, or of the image with the JPEG extension is not really a JPEG but a fake. Some editors are returning a file with the extension "JPEG", but looking at the image in Preview we can see it is a PSD or TIFF file. For example Luminar 3 used to do this.

How do you add a black line? If you edit a photo, you change the creation date, the file size, and probably the file format and the color sync profile. Simply exporting the same photo again from Preview with a different color sync profile should suffice. You should not need to draw on the photo and mutilate it.

What system and Photos versions are you currently running? Is you're bio at the bottom of your first post correct? Then Photos should be V 6.0 and all of the formats you mentioned are compatible.

Have you installed or run any "cleaning", "optimizing", "speed-up" or anti-virus apps on your Mac?

Boot into Safe Mode by booting with the Shift key held down and check there to see if the problem persists.  Reboot normally and test again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

> if the photo being imported is close copy of another image in Photos, it will tell you that it can not import the image because the format is ‘unknown’

Interesting. Have you tested what counts for a "close copy"? Same filename, same date or some same metadata? Altering a photo even so slightly seems drastic for a person that wants to avoid all unnecessary generation loss :-/

Properly formatted JPG and HEIC photos certainly can be imported, as can many RAW photos, TIFF, and PNG.

What sort of problems are you having?

Accepted where, by what?