You've got a book for a Singer and a box of attachments for a top clamp, so most of them will fit your machine. I only see a few side clamp feet. I must be getting rusty, I can't remember which one uses the "S" looking underbraider! OK- I looked at my pictures, that would be a National made machine.
I've not seen that round one before, but it does attach to the presser foot and has a needle hole. it's sort of like a super wide foot, but nothing like a darning (FM) foot. Most of those attach to the needle bar and don't use the presser foot at all.
The piece attached to the ring is how it clamps to the presser foot - just like all the other attachments have.