Yes, I have had a betta fish with a snail at the same time. Nothing happens the snail just slithers around the bowl and the fish pays no attention to it.

personal experience

Sorry but neither should be in a bowl. Both require a heat source and a bowl just doesn't have that option. Plus with bowls the water goes stagnant faster and with a snail in the bowl it will dirty up quick. Snails are neat but they can really be messy. I would urge you to consider getting a tank. 2.5 would be "alright" but not ideal anything else above would be better.

get a tank with a filter.
but yes most bettas will ignore snails but some will nip at the eggs

same experience , except with filtered 10 gallon

No, you can't.

However if you buy a 5 gallon with a sponge filter and a heater, you can.:)