Slant fin has "dummy" heat cabinets that are relatively inexpensive and easy to install if your original trim is in rough shape. Judging from pic, I'd say the room is part of a wrap around heat installation and is probably carrying too much element for the room, which you could remedy if you have access to joists below. Unless said room is on a slab. Looking good though.
No, I did it through the mail. As a non-res if you want to apply in person you have to go down to the Department of Public Safety, Special Licensing and Firearms Unit in Middletown CT. To do it via mail just call the Special License and Firearms Unit at (860) 685-8494 and they will send you a packet with all the forms.
Sorry but I cannot remember how much it cost, although it was under $100.