This is completely up to you. Most campers and instructors bring acoustic-style jazz guitars.
Extra guitar strings, a small portable music stand, pencils, a recording device should you like to record a class for your own personal use.
No. If you would like to bring a small amp, you may. Amps are not necessary unless you bring the type of guitar that requires one to be heard.
No. All activities will be in or adjacent to the hotel. If you would like to explore the area and/or go out to dinner, or if you have a guest, you might prefer to have a rental car. There is a light rail available from Denver International Airport that will bring you within walking distance of the hotel.