Of course, single-axle trailers cannot use X-chocks, but the point is to always chock the trailer before disconnecting the hitch or safety-chains. I witnessed a trailer roll-away from a TV and would have been a disaster and possible injury if the safety-chains had not still been attached..... It was a chore for the guy to get hitched back up to start all-over.
In response to the OP second question regarding the squeaking of brake-shoes while parked.... No, it's not going to cause undue wear or any hazard at all. (There's no actual pressure being applied to cause wear...or they wouldn't be squeaking!....because the wheel wouldn't be rocking.)
And, of course, never attempt to park a trailer with the electric brakes employed unless you wish to burn-up your magnets.