Does putting hot water make foot swelling worse or better?

Generally worse... Heat opens up capillaries and other blood vessels which allows more blood to enter the area. This can make swelling worse.
Depends. In the first 24-48 hours of an injury you would want to apply ice to reduce inflammation. After those initial stages when the maximum swelling has reached then heat would be good as the blood will flow and flush out inflammatory cells...
Usually worse... Heat usually increases blood flow to the area which may lead to an increase in swelling.