What treatments are required for my teeth/bite issues? (Photos)

If wires and brackets worked in the past, I think orthodontic therapy may be your best option. I would schedule an orthodontic appointment to determine if surgery is required. As you have already discovered leaving your retainer in a drawer will not help your previous orthodontic treatment. The black spots on your wisdom teeth could be cavities. I would schedule an appointment with a dentist as soon as possible to determine how much decay is on your molars. As far as your breathing issues go, a custom made mouth guard may help. Good luck with your treatment! 

If braces worked great before, I would believe that orthodontic therapy could again achieve the results you were happy with. You will have to be religious about wearing your retainers for the remainder of your life,or you already know what will happen.  You have a great deal of crowding and constriction of the arches. If you were happy with the results before which did not require surgery, you can likely get back to a point you are happy with that will not require surgery. I would recommend a thicker appliance like a nightguard to act as your upper retainer to help prevent constriction of your maxillary arch. The black spots are very likely to be decay. You should visit a dentist this week for an evaluation.

You really have a lot going on. I do think orthodontics and surgery are your best options. You may also want to see an ENT for your bgreathing problems. The best way to start is visit your general dentist and get the proper referrals.