not sure about the white specs, could you post some pictures of it? it could possibly be diatoms, which are good, it means your tank is cycling. have you added any ammonia yet? as far as using fish food for your ammonia source, i would use it as a last resort. not only is it hard to tell how much to use, but it takes a while to actually rot and produce ammonia and leaves a big mess in your tank to clean up before you add your fish. if you do not want to go out and find pure ammonia, i recommend using raw shrimp. i have not persoanlly used this method before but many on here have. i believe with your size tank 1 shrimp would be plenty of ammonia to cycle it. first, you need to get that liquid test kit we all keep mentioning so you can test to see how much ammonia you actually have, and nitrites and nitrates as your cycle gets further along. so glad to hear you will be cycling your tank fishless, it really is the easier way to go. your temperature is fine as it stands right now. that being said, when it gets cooler outside, like in the winter, your temperature will start swinging dramatically which will harm your fish. you should definitely invest in a heater by the time it starts cooling down outside. with your size tank you will only need a 50w heater which will be relatively inexpensive.
the thing about fishkeeping is you can't just look at it as another pet that you buy, feed, get shots for, and call it a day. fish keeping is most definitely a hobby. a hobby that requires time, patience, investment, and understanding. even experienced fishkeepers learn new things all the time. i definitely recommend to read all you can about the hobby and soak up as much information as you can. if you are like anyone else on this site that one 5gal betta tank will turn into 3 tanks in no time
it's a little thing we like to call MTS--multiple tank syndrome.