Hello,
Iraq is a cash society so people do carry round a lot more cash than we do in my home country. However home invasions in search of cash are common.
If you stay in an upscale hotel you can lock your cash in the safety deposit box.
Personally I do not go out with more than $200USD at a time unless I am making a specific purchase. I do wear a money belt around my waist under my clothing and carry no more than $100USD in my purse. I zip part of it in a purse pocket so it can't be seen and leave about 50,000IQD in my wallet at a time.
$100 bills are widely accepted as long as they are the newer ones 2007 or newer. $100 Bills must be in good condition to be accepted.
Sometimes ATM machines work here and sometimes they do not. Family Mall and Majidi Mall are fairly reliable for ATMs. In an emergency you can go to any 5star hotel and they have ATMs that take foreign cards like at the Rotanna Hotel.