If you provide plenty of cover, shrimp should be ok. I have a densely planted 20 gallon tank where many blue shrimp coexist with a betta and some barbs. However if the tank is pretty sparse (the way betta tanks tend to be) then it will probably eat your shrimp. Snails should be fine. The colorful ones, nerites, tend to need lots of algae to graze though. They might eat an algae wafer now and then, but they do best in tanks that have plentiful algae. Hard water is important to snails and shrimp, the calcium and minerals helps them molt and keeps their shells from pitting. Most tap water is hard in the U.S., if you have a water softener or naturally very soft water, that might be a problem...
Mystery snails ought to be ok. Some bettas will attack their antenna, but not all. Bettas are very variable in their behavior. I like females best because they're quick, but males with their long flashy fins, tend to be a bit slower and arguably more invert friendly for that reason.