to my knowledge, Shrimp always need salt, even if just a little.
Bettas are very tolerant of it, and tend to thrive in it. It helps their immune system as it is a natural antiseptic, and the little buggers that can cause your betta harm have less a chance of infecting your betta when the salt is present in the water.
The general rule is a teaspoon per 5 gallons. It is perfectly fine to underdose, but for your tank, the one full teaspoon should be adequate.
When changing water, it is best to add the salt back in as well. If due to evaporation you are adding water, the salt is still in there, so do not add more salt when adding water due to evaporation.