I believe in most older style dinettes the back cushion is indeed separate from the bottom and for a reason since usually the table is able to drop down and all the cushions used to form a bed.
If your fabric is worn out you may find the foam may have indeed also flattened out/broken down. It's your call but if you recover them you'll still have the old foam which may or may not have enough support to last much longer. Making new covers isn't hard but must be done exactly the right size in reference to the cushion or it will not fit correctly. Therefore unless you know what you are doing I'd leave it to a pro. The covers are actually almost too small for the foam so it will not slide around. And some companies do blanket the foam in a batting that will help prevent the cover from sliding around on the foam.
