Can't help with the specifics of your boat but:
See if you can drain the icebox into a small bottle like an old bleach bottle, just empty it periodically. This avoids putting any sometimes-smelly (from the odd spill or leakage) ice box melt water into the bilge. Years ago we had such a set up, the jug had to be emptied daily but it helped keep the bilges dry and clean.
Your head sink should drain through a through hull, I have seen sink drains teed into scuppers and/or intakes but don't think it's a great idea. Also, depending on your area you may be required to use a gray water tank which complicates things more still.
Odd that they installed a sink, but no water supply and no drain......
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)
1984 Fast/Nicholson 345 "FastForward"