I can't tell the exact size of those lines, but I think that you're right with the determination of what each is (A, B, C and D).
The humidifier and the copper condensate lines are apparently draining into a trap vented by the smaller of the two vertical PVC pipes and draining into the drain line (with the clean-out plug on it) under the concrete.
I don't know if that condensate drain is large enough for a washing machine drain, but it may be.
Check with your Building Inspection Department for local code. A washing machine drain may locally require only a 1.5" drain, or more likely a 2" line.
If that pipe that the condensate lines are into is 1.5", you may be able to just plumb an open top washer standpipe above it to hook the washer drain hose into, and connect the two condensate lines to the standpipe.
If local code requires 2", you're going to have to plumb for that.
Good luck!
Mike