Nope, the dog and cats and other varmints would have the virus-y garbage all over the neighborhood. The patient would have to keep it double or triple bagged in their room for 14 (24!) days.
Yes to burning everything later.
Yeah, why not. Tie the bags up tight, not going to make them any sicker. When they recover, set off one of these disinfectant flogger bombs in The room before going in