Can air purifiers be put on a wall and work for more than one room or do they have to be in a room to work?
I have 3 bedrooms in my upstairs, combined about 600 sq. feet, I just bought an air cleaner good for 780 sq.feet, can I just put this on a wall in the hall and if the bedroom doors are open will to work in all the rooms? Thank you.

Depends on the air circulation within your house. If you have forced hot air heating with central air conditioning then it would work better than if you had radiator heating and room air conditioners. In the later example, the effectiveness of the air cleaner would be significantly reduced because air circulation would be on a room by room basis rather than circulating throughout the house.
no as far as i know you can’t i would just put it in the hall and let it work its magic
well it says it will cover it all so yes give it a try before you buy one more. they may be exaggerating.