I agree on the cories, they must have a group (they are shoaling fish) but there really is insufficient space here; the Betta will be fine alone (snails no problem).
On the snails...these do not add to the bioload of the tank because they eat organics already there (fish excrement, dead plant matter, algae, uneaten fish food, etc) which breaks them down faster so the bacteria can handle them. These harmless snails (pond, bladder, Malaysian, whichever) are you friend in any aquarium.
Seachem's Stability is OK to use, I have used it. The Tetra SafeStart is probably better but as you have the Stability it will still help.