He looks like a Doubletail to me. Possibly a HMDBT? He has beautiful butterfly coloring. :) Yes, more plants, the better. If you give them too much empty space, they feel very insecure, they love hiding in plants and decor. He does look a little bloated. Bloated just means constipated. This can happen when you overfeed them. Since they're stomachs are the size of ONE of their eyes, it's VERY small. They will always look like they're starving, but don't give in!lol
I feed my bettas 4-5 pellets a day. I also alternate foods because they like variety. I give them flakes the day before I do water changes (flakes can cloud the water up) and I give them freeze-dried bloodworms the day before I fast them (this can give them bloat also). Bloodworms should be only given as a treat once or twice a week, not as a normal food. The pellets should be the staple food. Like I said, I feed mine 4-5 pellets a day (2-3 in the morning, 2 at night).
Just as a side note, you should only keep the tank light on for no more than 8 hours a day, bettas need a day/night schedule just like we do. Since they are warm water fish, you should also get a heater. The water needs to stay at 76-80*F. They also need a constant temperature, too much fluctuation can hurt them. Enjoy your betta, they have such amazing personalities!