Do I need to register everyone staying at the property? Yes. Everyone staying at the property must register, there is the second form for adding multiple people to the property if you are doing it at immigration.
Do I need to register if I am living in my own home? Yes. If you are a foreign national and own your home in Thailand, you must register your occupancy.
Do I need to re-register if I have been out of the country for a couple of days? Whenever you leave the country, you must re-register upon your return.
Do I need to register if I have been on holiday and stayed at another hotel/guest house? Yes. The owner of the hotel/guest house will have registered you as a guest of the hotel/guest house. Once you return to your primary place of residence in Thailand, you must re-register.