well, first of all, my deepest apologies for having to resort to posting here

j/k
it seems you are correct with the fact that the device is indeed syncing, or trying to, as the arrows going around in a circle is an indication of such. the other spinning item is the device working on something that will most definitely cause drain as well
i think we're going to need more info; actual device, iOS beta attempting to be put on, is your UDID registered? whatever you can provide would be great!
my initial response would be "restore as new" NOT from backup but maybe even just a simple reboot would fix it. sometimes trial & error is the only option