In how many months will a gap close when having braces?

Depends: Depends on gap size and degree of torque that is being applied along with your tolerance level. Best to speak with your orthodontist.

Depends: Depends on age, overall general health, oral hygiene, health of your gum tissues, health of underlying bone, severity of the malocclusion, "gap" closing mechanics, care to not damage the Orthodontic Appliances, but most of all the training, experience, and skill of the Dentist, or preferably, qualified Orthodontist. See your practitioner for a knowledgeable answer.