large water changes, 100% if necessary, is EXACTLY what you want when a tank is cycling. i'd rather have a tank's cycle take forever to complete than have my fish being poisoned by ammonia or nitrite. the good bacteria do not live in the water, they live on surfaces in the filter and in the tank.
Prime will not affect your nitrate reading. water changes affect your nitrate reading, by removing nitrates when you do a water change. you don't need the Stress Coat at all. too much crap being put in the tank is not good. none of my tanks have seen anything other than Prime for a few years now, as far as additives to make the water safe go.
herniation of the muscles around the anus is common in fish that are very constipated. he may have that white bump for life now, or it may subside once his system is back to normal and he isn't constipated any more. as long as he's eating, swimming, pooping, and generally looking 'happy', i wouldn't worry.
anything marketed for use with bettas is an absolute case of the manufacturer trying to cash in on the 'betta fad'. you don't need betta products for bettas. the only thing i advocate that is a betta product is the Betta Revive, and that is because it has worked so well for me. if it was called 'gobblygook fish stuff' i'd still use it and advocate it, lol. what i'm trying to say is that 'betta vitamins' are bunk and a waste of your money. fish receive their nutrition via their diet, and feeding a high quality and varied diet is key. my bettas have always had a rotation of betta pellets, freeze dried food, frozen food, and veggies (peas, and zucchini when i feed it to my bn plecos - the betta tends to munch on it too). yes, i keep bettas in community tanks. they are fish, and don't need to be treated any different really.
as for the white powder in the tank, take a picture of it so we can help determine what it is.