They can get nippy if they're not in a good sized shoal so I wouldn't risk the Betta in there. You can easily bump their numbers up to 6 though to make them happier! They will display to each other and it's super adorable! They will often spar with each other which will also stress out the Betta so in any situation, I wouldn't put the two together. But I totally love the idea of just having Phantoms in the 10 gal, they would be great! You could get a snail as well if you wanted, but just one, preferably a Nerite if you can find it. I know big chain stores don't often sell them so if you've got some small local stores around, they might sell them.
Nerite's poop less than other snails and they can't breed in freshwater which means they won't take over your tank like other snails ^_^
Rembrandt II, Suiché
Leopards: 1:4 Hawkeye, Luna, Astrael, Dorian, Cullen
Gargoyle: Cloudjumper and Toothless