The holes in the shell may be to reduce vibration by reducing the propeller blade excited pressure force variations on the hull either by "tuning" the internal void or voids to counteract the propeller pressure forces or by actively pressurizing and depressurizing the internal void or voids in a phased relationship with the propeller blade passing frequency to cancel out the pressure pulses. Then again, it could simply be that they did not need the buoyancy at that location.
I'd just assumed inlets for cooling water but I don't really know.
This is an educated guess on my part. The ship pictured is a speciality bulk carrier designed to deliver cargo in shallow water ports. The normal ballast suctions and other sea water suction locations along the forward areas of the hull would be exposed after cargo discharge, therefore the suctions were located in the stern frame aft to insure an adequate supply of sea water.
Are these holes for box coolers like a Wika style coolers?
The holes appear to be keel coolers albeit an interesting arrangement.
I think those holes are part of a system (includes valves maybe) that entrain air into the water flowing past the stern in an effort to induce separation. When a vessel moves through the water at high speeds, the hull creates a "hole" that fills up with water and creates a pulling force in the opposite direction. The entrained air helps break that down and probably increase speed and fuel efficiency. Just a guess...
I believe they could be for a box/keel type cooler for the steering gear hydraulics.
I do suspect it may have something to do with propeller /cavitation induced vibration ...
The holes located there shown in the picture, in case the ship is a chemical tanker usually they are there in order to mix oily mixtures allowed to be disposed in the sea in order to prevent the formation of a film and to mix it with sea water to form small bubbles in order for the fish to eat on. We are talking about vegetable oils oily mixtures. Another senario is for the disposal of sewage in order to help them dissolve.
More pics below, from International which coated the ship with Intersleek 900.