lowest lvl a char can be stolen from i believe is 12... or somewhere around there... maybe 10?  but yes, there is a specific lvl.
as for robbing, the house you start the game with cannot be robbed by players, but as soon as you buy a new house in another district, it can be robbed.  if, however, you stay in your original house too long (i believe around lvl 18), city guards start taking things out of your house.
--jason