Feeding once a day can easily cause bloating/constipation, etc.. as mentioned earlier feeding small multiple times a day, at least twice, is the most recommended way of feeding. Feeding once a day will either over feed, or not provide enough nutrition.
A betta can go around a month without eating, but the danger zone starts at around 2 weeks. A 2-3 fasting is normally recommended with bettas who may be bloated/constipated. It is safe, but your guy may not like it.
Go ahead and do the 100% to clean out the home tank if you have medication in there.. or if you have a carbon filter, you can place the carbon back in and it will remove the medication- just change out the carbon filter afterwards.
For cleaning a 5 gallon properly it depends on whether or not you have live plants, as that will determine just how much water to change each week. Along with your cycle (since we know it isn't cycled at this point).
Once you fill up the tank with new water (if you go that route over the carbon filter), you will want to test your water on a daily basis over the next 4-6 weeks- or if you do not have a liquid test kit and can not get one, Petco/Petsmart tend to test for free. In that case, I would take it over there as often as you are able to during the week. As tanks that are attempting to cycle can and do have spikes in the chemistry, such as ammonia, which can be harmful/deadly to fish.
Fish-in cycles tend to be hard on a fish, but it's doable.
If you test for ammonia during the 4-6 weeks, you will want to do a small water change to bring it down.
Here is an easy guide to cycling
.. it's not really all that hard, just takes some time and commitment.
On a normal cleaning schedule (with no live plants.. if you have live plants let us know how many) for a 5 gallon you are looking at roughly 30-50% per week of a water change. When doing the weekly water change you are going to want to vacuum/siphon the gravel (I would but a small siphon
you can get fairly cheap).. as filters don't remove the waste, but rather hides it.
So use the siphon each week to vacuum the gravel in the tank, only take out 30-50% of the water while doing so.
When replacing the water, use a glass aquarium thermometer to get the temp of the new water to be the same as the old water. A lot of people use buckets to carry the water in, so you can get the temp just right.
When done filling the tank back up, put in your water conditioner for the whole volume of the tank.
I recommend removing your betta during this process, to reduce risk of chemistry change shock (to put it in layman's terms).. use his cup you got him in if you have it.. after you fill up the tank, remove a bit of the water from the cup and replace it with water from the tank.. let him adjust over a 10-15 minute period, removing/replacing the water a total of at least 2 times.
Clean out your filter media each time, swish it in old tank water you had siphoned to get rid of trapped debris.
Carbon filters should be changed monthly, sponge filters should be changed once it starts to fall apart.
That is the recommended water change schedule for a tank your size, non-planted.
I would also recommend using a sponge as the baffle..
Your pellets aren't necessarily bad, but the protein is a bit low.. continue with pellets, but I recommend Omega One Betta Buffet or New Life Spectrum Betta pellets.. as mentioned prior by callistra.
I personally prefer the Omega brand.. I use those in between live foods and home made betta food.. and for my picky eaters who will only eat pellets.
Good luck and any more questions please feel free to ask!