As far as neons are concerned, I have seen them in 10g tanks and I personally don't see an issue with it. Some people disagree, to each their own. It all depends on what you are comfortable with. If you are able to find fish like ember tetras or chili rasboras, for go it. They are great little guys who do very well in 10g tank. There are a good share of other fish too. But, as fish keepers, we don't all agree on things like tank size. I also have no issue with a dg in a 10g tank, but some people do. As for the betta and neons, if a betta is community friendly, it is going to be fine with neons.
As for the fish-in cycling, it can be done with almost any amount of the stock in there, just keep in mind that more fish equals more water changes during the cycle. For schooling fish, most will be fine if you start with like 3 or 4. I have kept plenty of under sized schools in quarantine or while waiting for another shipment and I have not had an issue with them stressing out and dying. With neons, I don't think it's a concern for this case.
If you are more comfortable with fish besides neons, look at green neons, micro rasbora, celestial pearl danios, ember tetras, jellybean tetras, scarlet tetras, and least killifish. In addition to those mentioned by others, there are also dwarf cories, Asian stone catfish, croaking gouramis, pygmy sunfish, pygmy killifish, and shell dwelling cichlids to name a few. Of course, most of these nano fish are going to be more expensive and harder to find for the average aquarist and would probably need to be special ordered. I have done a small tank with just guppies and it was fun and colorful.
EDIT: Sorry, but mollies get too big for a 10g tank. They can easily reach 4 inches.