It's not unusual for a new betta to not eat much, if at all. I'd suggest trying to give him a few frozen blood worms and see what he does with those.
I know the type of lighting you are talking about. My b/f raises cichlids and has a pretty advanced led lighting system on his 150g tank. When we cycle the lights from color to color it seems to really agitate the fish. I think the same could be happening with your betta. Try leaving it set on just one color... I'd suggest blue. If you must light the tank that is. Otherwise, I see no problem leaving him with just the natural lighting that he would get. Where we think it's cool to have a light changing from color to color all the time, imagine all the lights in your apartment doing that. All cycle together from green to red to blue... uhhhhg!!!
Do you keep him close to the window? If not, try to leave the blinds cracked for him. Also, even with blinds, if he is near the window, he could get over heated.
Also, IMHO... 100% water changes are extreme. It removes all your beneficial bacteria. I'd go to 2 50% changes per week. Other folks will have diff opinions on this I know. And when you do your water changes, leave him in his container. Remove the water you want to change using a turkey baster. Then replace with conditioned aged (set out for a day or so) water. Add the water back gently so as not to knock him around. And add it slowly so as to not change the temp in the container more than a degree or so.