Apparently, northern Iraq is within safety limits but Baghdad...
Someone gave you bad intel. Really bad intel.
Northern Iraq still sees plenty of action, albeit not what it once was. Baghdad still has kidnappings, bombings, shootings, grenadings.
I've overnighted in Iraq many times. Then again, I've taken rocket and mortar fire while overnighting in Iraq many times, too.
I commercialed into Baghdad once, and was picked up by a driver in a heavily armored suburban. We took a different route, and when I queried, the driver mentioned that the route we normally took went under a small underpass. The previous day a vehicle suffered fatalities under the underpass, when someone standing above dropped a hand grenade on them.
Events like that are common, and not unusual.
Iraq is the kind of place one invades. Not that one stays, especially if one intends to remain "outside the wire."
What are the special procedures/restrictions there?
Not if you're flying in as a commercial operator. Standard ILS approaches.
...and how about a nightstop there? Would you have any issues to enter the city?
Issues? Yes.