Looks like your wood may have warped or moved. Without seeing it in person I am not sure how to tell you to proceed. The hinges may have given in and caused the movement, but again I cannot tell by the pictures. If you want to keep it original.......don't touch it and keep in the corner. If you want ot make it useful, I would start with the hinges by replacement them. See how the jaws line up after you remove the hinges. Start here and move forward.
Maybe you can plane the bottom thickness without touching the actual jaw closure. As for the jaw, you can just glue some 4-5 oz veg tan leather to protect your projects while in use.
Good luck!