I live in a compound and yes we have to pay our bill, though my water and electricity bill is max 250 riyals. Telephone, adsl and cable tv(mosaic) is 250 riyals(in all).
There are two american schools here. The American embassy school is near the Al Sadd stadium, decoration roundabout and yes it is a good locality with lots of compounds around it. Average rent will be 15k per month.