Dwarf shrimp actually prefer cooler water, between 65 and 75 degrees Fahrenheit, so a heater is not really necessary for them if they are in a heated room.
As for the betta tank, If it were me, I would get a 5 or better a 10 gallon starter tank for the betta, myself, these are more appropriate than a one gallon, very common, and a good value.
The absolute minimum recommended size for betta tank is 2.5 gallon, but 5 or more is really much better.
If it is a current setup, I would change about 80%-90%
Of the water twice a week with a tank this small, or in other words, just leave enough in the tank each time that the betta can still swim upright.
With such a small tank, it shouldn't be too much work.