Betta Fish: New tank setup, first-timers looking for feedback.

Hi everybody, I'm looking for opinions and feedback!

First off, should lead with the fact that neither my wife nor I have ever owned fish. However, our son wanted a fish for Christmas, and had been asking for several months leading up to the holiday. So Santa brought him a fish tank with all the necessities and a note explaining that Betta Fish prefer warmer climates than the north pole and that his parents would take him to pick out a Betta Fish once it's new home was ready for it. Since then he practices (mimes) feeding three tiny pellets, one-at-a-time, faithfully, twice a day and turns the light on and off in the morning and before bed.

So here's our 5 gallon Betta tank, we bought a used filter from the local mom 'n pop aquarist shop to get the good bacteria jumpstarted into the ecosystem, as well as the water conditioner and bioculture starter chemicals and have been using as directed. Additionally, we got the Java Fern, Water Sprite, and Red Root floaters (I want to get an Anubis or Pothos or something to replace the silk leafs on the left side, so we're 100% live plants.)

So far I'm cautiously optimistic. We've been cycling for about two weeks now. Daily water tests indicate Ammonia, Nitrates and Nitrites are all steadily within recommended spec (0/0/<20). Temperature seems parked at 77 with the heater on, which is annoyingly close but on the low edge, and Carbonate Hardness is only at 40, so I'm getting some crushed coral to help raise it to 50 (and replace the large white coral chunk in the back that we foraged from the beach last summer). Everything else is comfortably in the ranges recommended from any of the guidance I've seen.

But the real reason that motivated this post! We seem to have picked up some hitchhikers, I assume from the plants. Three days ago we spotted a snail on the front glass and later doing a backstroke across the surface of the water. Two days ago we realized there were actually two snails… we got a photo of them… well… working on making more snails… Or fighting if you asked our son what he thought he saw. I think these snails grew from eggs, as we definitely would've seen them sooner had they been this size two weeks ago.

My questions…
1. Can anyone help ID the snail species? We would love to learn more about them. They're less than the size of a pea, dark colored shells with some patterning (see photo) and purple-ish foot when back lit.
2. Can we assume the snails are a pretty good indicator that we're on the right track with the water quality and tank ecosystem? I've heard Bettas might eat snails, sad, but ok, any other risks of leaving the snails to cohabitate with a Betta?
3. Any opinions from the veterans on the plantings/cave decor/driftwood setup?
4. Any other tell tale signs we should check for before we start planning a trip to the shop to pick out a fish?

Thanks!!