If my mom is 5'5 and my dad is 5'6 what will be my permanent height? I'm 5'1 now at 17 but im not sure if my bone plates are closed yet

Probably 5'1" The height expected from any female offspring is the average of both parents less 2.5 inches, give or take an inch. At 5'1" and 17 you may have a little growth left, but I wouldn't expect much. If you have not grown more than a half inch in the past year You are done or close to it.
No way to tell. A bone age x-ray may give your pediatrician some information about any remaining potential growth.