I'd like to start by saying that if your tank is 2 gallons in size, you probably shouldn't have any other tankmates. Tankmates that are fish, at least. Not only are you exhausting your bio-load and having to deal with mass amounts of ammonia production, but tetra and corydoras are shoaling fish and should be kept in groups of at least six and three, respectively. Otherwise they will not be thriving, unfortunately. You should consider ADFs, snails, or shrimp for tankmates.
On to your issues! First: what exactly is the pH of your well water? It can certainly be alkaline without being a problem - your betta can handle it, for sure. Same if it's acidic. Odds are you won't have to adjust it. And quite honestly, you shouldn't. Altering your pH could be disastrous and sounds like it already has been. The more stable it is, even if it's a bit alkaline or a bit acidic, the better. Just stable.
And lastly: No, two gallons is not too small for a heater. There's a Tetra Whisper heater at Walmart that many people here use in their tanks. Keeps the temperature at a stable 78º for most, though it's not adjustable. There's also the Hydor Mini Heater, if that's more up your alley. Really doesn't matter which as long as you have one. Bettas are tropical fish and truly thrive in warmer waters.