Do symptoms like ankle pain go away quickly?

No. Unless you had a recent injury (mild sprain), ankle pain usually persists a long time because of the type of problem usually relating to arthritis or bone spurs at the joint (just to name a couple of many options).
No. There are many causes of pain around the foot and ankle so the duration of symptoms depends on the diagnosis and the treatment.
Depends on Cause. There are many possible causes for ankle pain. Some are self limiting and can resolve in a short time - others can be more troublesome. If the pain is persistent you should be evaluated by your pcp or by and orthopaedic foot and ankle specialist.