Welcome, and welcome to being a new betta owner.. be careful, they can get addicting lol.
Be careful with putting it near the space heater, as the heater turns on and off which could cause fluctuation of the temp and is more dangerous then cool temps.
If you can't get a heater right away, then I would get a glass in-water thermometer, usually less then $2 for one- that way you are aware of the temp, and when you do a water change you can get the temperature as close to 78*F as possible.
For a heater I would look for one that is 10-25 watt- preferably adjustable, but if not, something that fits into your tank will be fine. Having temps in the lower 70s won't kill the betta, but may cause long term problems, such as lowered immunity, lethargy, slower metabolism and with all that it could shorten their life spans.
So it's ideal to get a heater once you are able to. A small 10 watt is usually around $12, so it's not too bad- I'd shop around and see what you can find that works best for you.
A 1.5 gallon is a suitable home for a single betta- make sure to have a silk plant or two and if possible, a cave of sorts for him to feel secure and to give mental stimulation to them... they also love to sleep in the plants and in the cave.
To clean a 1.5 without a filter it's ideal to do a 50% water only, and a 100% water change per week- you may be able to get away with a 100% every 4 days.
You will want to scoop him up using the cup he came in and change the water- adding in the new water at roughly the same temp as what it was, and adding in the right amount of water conditioner for the volume of the tank. Float the guy in the cup for roughly 15 minutes, halfway through remove some water from the cup and replace it with water from the tank to acclimate him to the chemistry while he is acclimating to the temp.
As for feeding, small meals multiple times a day is the best- I tend to feed mine twice a day, morning and evening, once in a while a snack mid day is thrown in as a treat- you can fast them for a day out of the week if you wish as a lot of people do. I personally don't because I am very specific on how much I feed, and I vary the amount daily and instead of a full day of fasting, once or twice a week I will have them skip a meal.
Pellets tend to be the easiest to feed- common pellets a total of 4-6 a day is fine, so 2-3 pellets per meal. Or a few flakes per meal works.
Once a day normal feeding, I don't personally like it because my view is that the one meal you are either over feeding per meal which could cause bloating and constipation, or underfeeding and not giving them enough nutrition. But skipping a meal here and there won't harm them as they make up for it the other days.
Welcome to the forums once more and please feel free to ask! If need be, you can start a thread with your questions, you may get more people seeing it as a lot of people don't look up at the stickies :) And don't feel bad, most of us have listened to the myths and pet store employees with our first bettas.