In a tank that size, you will need to do a 100% change every two days. I realize this sounds excessive, but keep in mind that this tank is simply too to be cycled with any real stability, and all uncycled tanks need frequent 100% water changes. It is a very small container, and since you are used to keeping koi, you know how much waste fish can put out and that it can reach toxic levels surprisingly quickly.
I recommend ordering a 25 watt adjustable heater--I prefer to do all my shopping online here: http://www.fosterandsmithaquatics.co...lies/pr/c/3578
since their prices are way cheaper than you'll find in a pet store, even with shipping included. If you want to get one from a pet store and they don't have it in stock, don't be afraid to ask them to special order you a 25 watt adjustable heater like the Hydor Theo, many times they'll put your request in a special order book and have it for you in a week or so.
If your mother is against you getting a larger tank, I highly recommend getting a live plant or two. Plants consume ammonia as their food source, so stuffing as many plants in there as you can will be very beneficial to your water quality and give you a greater margin for error in case an emergency arises and you have to skip a water change. Plants don't really give you a get out of jail free card for water changes and you should still strictly adhere to your schedule of 100% every two days, but they will certainly help. Good plant species to buy are java moss, java fern, anubias, and elodea/anacharis. Always do your research before buying plants, because many pet stores sell non-aquatic plants as if they were aquatic. Non-aquatic plants will drown and melt in your water after about a month, making a big mess. You want to avoid that. :)
As far as the food, I don't recommend freeze-dried foods. They can cause terrible bloating and constipation. I don't use them at all because I've had bad experiences, but if you do choose to use them, use them very sparingly as a treat and always soak any dry food (pellets, flakes, freeze-dried) that you give your betta in a bit of tank water until it's completely saturated. Bettas were not designed to eat dry, air-filled foods--it's kind of like when humans eat uncooked rice, it expands in the stomach as it takes on moisture, causing bloating, discomfort, and constipation. Try to avoid that. You should consider varying his diet with more nutritious pellets such as OmegaOne Betta Buffet Pellets, Atison's Betta Pellets, or New Life Spectrum. Frozen fish food is another great option that provides your fish with a lot of protein and lasts a long time. Most people use a mixture of pellets supplemented by frozen foods--typically you should feed your betta two pellets twice a day or three pellets once a day.
Welcome to the forum and good luck with your new fish.