The recommendation given to you on proper changes for a 1g is incorrect. There is a sticky at the top of this section that provides the ideal water change schedule/% based upon your set up.
For a 1g, unfiltered tank you really only want to be doing 1 50% and 1 100% water change per week ideally. There is such a thing as too clean of a tank, too sterile.. like us and all other creatures, they should be exposed to certain elements and bacteria, which cannot grow properly in a tank that is too sterile.
Tap water is preferred as it has the right minerals needed that a lot of filtration process removes.
Next to water quality, warmth is very important. You can find small heaters for your tank, anywhere from 10 - 25 watts would be recommended for the 1g. It may be a bit difficult to find a mini heater, but it is possible.
Again, don't change the water as often as stated... here is the link to go by
, it was created by a member who has decades of care/breeding of bettas, and I too have two decades of tropical fish care where I can safely say that these recommendations are on the ball.
I have tanks that range from 32 ounces to 30 gallons, I use a lot of half gallons and 1.75 gallons.. I base my cleaning partly on OFL's recommendations and my own testing/set up. I personally only do 1 100% every 5 days on my 1g and 1.75g. You do what you feel is best for your fish, just make sure to at least clean it once a week to keep him healthy and happy :)
Good luck with everything :) I hope he loves his new fish!