unless the red bulb was for heat it's no big deal that it burnt out. as long as your uth is working and the temps are right the red bulb being out shouldn't matter.
mine tries to climb the glass pretty often, so i wouldn't worry about that too much either. i think they just want to explore and get bored being cooped up, if it's in a new environment it's probably still adjusting to were things are.
I've heard it called glass dancing with Beardies. None of my geckos do it. One does look out though. I think some of the time she is trying to investigate her reflection :main_rolleyes: