Hope I have been soom help. The park requires an application. Applications for winter hikes and climbs are accepted only after November 1 of the year you plan to climb. The application form asks for proof of qualifications and experience, and you must have at tleast 4 members in the ascent party. All members must file an application.
Camping is permitted but limited to designated sites.
There are shelters along the AT and the Sperry Campground has 34 tent sites and 5 group sites. If your goal is to do the highpoints recognized by the State Highpointers Club, then Yes, you do have to do Boundary Peak. Prior to more accurate surveys, people believed that they had reached the highpoint of CT once they had reached the summit of Bear Mtn. I believe that a sign atop the summit may still indicate that this is the case. This is a bit higher than the summit of nearby Bear Mtn.