I'd keep it on the side in case the water bowl got sloshed out etc.
Humidity isn't dependent as temp measurements on location though - you wouldnt have to deal with any sort of equivalent of a thermal gradient (heat rising vs floor temps etc).
Yes it is! (the velcro idea). I had to velcro mine because Kashmire kept knocking it over. Now he just uses it as leverage when he wants to explore, and it stays put!