“Do gum abscesses go away on their own?”

It depends on the origin. If it does it usually recurs unless you get treatment.

No, the infection needs to be taken care of for the abscess to go away.

Not usually, typically an acute gum abscess is manifested due to some foreign object that has gotten trapped under the gum line such as a popcorn hull or the like or possibly due to chronic debris such as plaque or calculus that is trapped again under the gum line both of which result in inflammation and eventually infection as the body's way of dealing with the foreign object. If not removed the foreign object will eventually cause gum abscess and eventual bone loss until removed either by the patient with regular oral hygiene or if needed by the dental professional using dental instruments such as scalers and or sonic devices which in some cases may require anesthesia. In some cases a gum abscess can result from a tooth nerve infection that can also infect the surrounding gum too, in that case root canal treatment will be required to resolve the infection. A dentist should evaluate the problem to determine if it is a gum origin problem or a tooth nerve origin problem so that the correct treatment can be initiated to resolve the infection.