Hey!
I know exactly how you feel! Sometimes it feels like you're trapped :/ but dont worry I have been in this situation so many times and never got sick. Anyway as far as your questions, its important to know that people CAN be contagious up to two weeks after symptoms stop, HOWEVER that is only through their um..waste. So as long as your friend/ mother wash their hands well after using the bathroom, they should be perfectly safe. Most people stop being contagious after 3 days anyway
As far as your house, noro can last for a while in carpets but again, as long as you are washing your hands before you touch your mouth youre totally in the clear! Just try and not use the bathroom your mom was using while she was sick (if thats possible). You'll be fine!