Your betta would be very happy in a 5.5 gallon, that's the perfect size for that type of fish. As far as shrimp, you could add one, but I don't know much about them.
That sounds fine I have two betas and I don't have a filter or a heater for them so you don't even need those. That will free up more space, I am pretty sure that the shrimp will be fine check with the store attendants. Snails would also work you could buy just one.
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