The floatiness could be from constipation as Alyssa has linked, or it could be dropsy. Dropsy is difficult to bring a betta around from, but not impossible. Dropsy is a condition that occurs when bettas are kept in overall poor conditions .
You need to get liquid test kits. API makes good ones and they should be available at your local petsmart. You can get a master kit, which will include a PH kit, which you should have as well as ammonia and the others mentioned.
You should not keep live plants in the tank without appropriate lighting. They will die off and as they do it will deplete the oxygen, especially without some sort of filter or airpump. I use sponge filters with an airpump on my betta tanks. Even with lighting, there is a normal amount of die off from plant life, and this must be removed.It can cause an ammonia spike, or even alter the PH.
One small pellet a day is not enough food. 3-4 is better, skip a day on occasion. Sometimes bettas can become sick and get infections from poor water quality. In such a small unfiltered tank you should change 50% of the tank or more per week or even twice, with water that has been left to sit a day inside, or insure that the temp of the change water is the same as the tank. When you change the water you should be siphoning out waste. This is very important. You should have a thermometer. Bettas do best at approx 78-80 degrees F. To keep the tank stable, use the heater. As the house warms and cools off at night, the tank fluctuates. It is the stability that will keep him healthy. Do you see any other outward signs, or just the lethargy and floatiness?