Okay.. now I will read your post.. but had to answer the question at the top first, as all bettas are crazy ;)
He most likely is enjoying the room, enjoying the exercise, and looking at his surroundings outside of the tank. I have a boy, perfectly happy that swims nonstop- tires me out watching him.. but just the way he is.
I say just make sure to feed him small meals a couple times a day to keep up with the energy he is burning and let him just be him.
He doesn't need more plants.. in my own personal opinion. Yes, some prefer a more planted tank, but not all of them do.. If all he is doing is swimming around, then it's a good sign as he feels secure and is happy in his own little territory.
Now, don't get me wrong, you have gotten some good advice about more decor.. but honestly, it's not truly needed to keep a betta happy/healthy.. all depends on the fish, and if he isn't being shy, acting stressed then no reason to change it unless you want to. There may be something outside the tank in the room that attracts him to cause him to swim on that side more.. who knows.. but if he seems happy and active, then keep it as you like :)
As for reflection on the glass- that tends to happen when you have the tank light on, but the room is dark. And a good flare a day is good for them.
Good luck! And congrats on your new little guy!