congrats on the mantis, but i dunno... i cant really trust that you actually have one without some pics!
1. i dont think its a problem. one of two things are happening. hes just figuring out where the tank boundaries are, or hes challenging his reflection in the glass. nothing to worry bout.
2. specific mantis worries are shell disease (treatable), algae growing on it (very often fatal), or the mantis sitting out in the open curled up in a tight ball all the time and not just as a response (often fatal).
3. here's a link with the best mantis species info available. read it. according to it P ciliata will burrow under the rock, in the sand. so i would go with a sand bed of at least 2 inches but preferably 3-4. in the short term, BB will be fine.