If you have a private room it's shouldn't be a problem but I know a lot of places they say the bathrooms are just for patients in the rooms. Best to ask. Mine always just went home for a bit to shower and eat and grab anything I wanted even though I always get a private room.
Mine was able to. And i am sure they can at this one too just because they keep you for at least 2 nights.
Depends on the hospital. Mine allows it but it's something that you'll probably have to ask about.