First, welcome to Tropical Fish Keeping forum.
Well, you are learning one thing the hard way, but it is a very important lesson: always research a fish before you acquire it and know what it requires (water parameters, decor) and its personality and compatibility. That is key to a healthy successful community tank.
Betta will readily eat neons if they feel like it. I personally think a betta is a stand alone fish in a small aquarium (5g is ideal), with perhaps some bottom fish like Corydoras or shrimp. And live plants.
The picture is blurry but the "unknown" fish appear to be characins (tetra), I'm thinking one of those "berry" things, like Blueberry or Strawberry Tetra. They are artificial fish derived from (if memory serves me) the Blackskirt tetra. These can be nippy. I don't condone buying them.
No idea what a see-through fish might be, but obviously that could be another source of trouble until you find out what it is and learn its habits.
If this tank is actually 5 gallons, it is too small for any of these fish except the betta alone. Tetra need to be in groups, minimum 6, and there is not sufficient space (in terms of physical swimming room but also and perhaps more significantly water quality resulting from so many fish) in a 5g for any tetra except the dwarf species like Ember Tetra
. But they would very quickly become food for a betta.
As kitten correctly mentioned, the above issues can easily cause stress and that weakens a fish's immune system leaving it vulnerable to various health issues and even demise. So as for the neons disappearance, it could be cannibalism, stress (other fish quickly consume a corpse), water parameters (no mention is made of pH, hardness or temperature).
You need to work out what you want in this tank; the store may exchange fish, they understand these difficulties we get ourselves into. The betta on its own is one option, or without the betta a small group of a dwarf fish, there are several in the cyprinid group and the Ember Tetra
I mentioned. Have a look at our fish profiles (second tab from the left in the blue bar across the top), all these issues are mentioned for each fish species. And we are all here to offer guidance.