There are no real laws concerning overnight parking other than many businesses don't allow it on the parking lots so observe signs posting such. As for turning off the engine, its fine if youre in Florida this time of year but if youre up North, turning the engine off and you just might freeze to death so a lot of this is just simple common sense so if it doesn't feel right, youre probably right so move on and find another place, and above all remember to lock your doors