Is it possible to get periodontal disease at age 12?

Yes. Periodontal disease is not age specific. Improper oral hygiene can lead to periodontal problems as well as decay in the young patient. Crowed teeth can also contribute to periodontal problems in the young patient. Juvenile periodontitis is a more severe and aggressive form of periodontal disease if left undiagnosed and untreated that can lead to premature loss of teeth.
Yes, but... Not all forms of periodontal disease are the same. There are multiple forms that are very destructive at young ages and are due to specific genetic alterations. Some of these forms of periodontal bone loss present with other medical problems. Some forms also show specific patterns and rates of bone loss.
Yes, but not common. My colleagues already gave you some excellent answers. While possible, more likely associated with some medical problems such as diabetes & autoimmune diseases. I have never seen it myseif. If you have concerns about your own mouth, ask your parent or guardian to take you to the dentist for a checkup to make sure your teeth and gums are healthy. Even if not, early treatment makes a big difference.
Yes. Stage I gum disease is common. A rare condition called juvenile periodontitis is rare, but ver aggressive.