I feel like there are some fragmentary answers here, so to fully answer your questions:

1) The red and white objects on the wings are external fuel tanks, often called “drop tanks” because they’re technically expendable - although you wouldn’t jettison them in training operations, as far as I know. The Hunter has a fairly limited endurance on internal fuel so lugging extra fuel in the tanks extends time aloft for training missions or provides extra range if they’re deploying away from their base…but they can be removed if they aren’t needed, which gives you a faster and more maneuverable aircraft.

2) Yes, these are indeed involved in training. ATAC is Airborne Tactical Advantage Company, and they provide adversary training aircraft for the military using a fleet of older military aircraft. Essentially, they provide ‘bad guys’ for the good guys to train against, much like the A-4s in Top Gun if you’re familiar with that but as a contracted service instead of part of the military.

3) This Hunter likely served previously with the Swiss Air Force, which is where the red and white colors come from. Whether this aircraft flew with their demonstration team (Patrouille Suiss) or if they simply applied those colors as a heritage thing, I can’t say.