If you look
at the photos I linked, that is the forward end of the CB - the part that stays up in the trunk regardless of whether it's raised or lowered. The large through hole in the middle is where the pivot pin goes through, and the other lower hole (large on one side, small on the other) is where the downhaul attaches by feeding the line through the smaller hole in the edge of the board and burying a stopper knot in that cavity.
As for your questions, I'll actually start with B first. The process is essentially the same, but the exact steps depend on your boat:
1. As I said, I did not understand the instruction about doing it with the CB in either. Maybe someone else has done it but I couldn't figure it out. You don't have to get the whole board out, but you do need to un-attach it and drop the forward end at least a few inches. So the first step is to get the boat in a position where this is possible. Depending on the configuration of your trailer bunks, frame, etc., if you can do this where the boat normally sits or by shifting it a little ways in some direction, that's easiest. It's OK if the aft end of the board won't drop - you just need to be able to get the forward end down a little. If you can't get this done on your trailer, than you have to careen it or at least put the stern on some sawhorses or something and get the boat far enough off so that you can then remove the board. That is the point of careening, to make it easier to get at the board (to answer your question A).
2. Figure out how your board is attached. Mine had the two steel plates that hold the wedges and pin up in the trunk. Those are screwed in from the bottom of the hull so you just take out all the screws . However, I believe some DS IIs had the CB attached with a pin that went all the way through the trunk and with fastenings in the bilge. So instead of removing screws and plates from the bottom of the hull, there would be nuts to remove on sides of the trunk inside the hull that you should be able to access through the two deck plates in the forward end of the cockpit (I think, I've never actually worked on that kind). Either way, if the boat is upright, FIRST prop up the board so it doesn't drop and break itself or your face! It weighs about 25 pounds. THEN remove the fastenings that hold in the CB. If the board doesn't come out there is probably some old caulk that needs to be pried out.
3. Drop the board enough to get at the old downhaul hole, pry it out and clean out the hole, and replace the line and plug it as Tim said.
4. Put everything back in reverse order.
Once you get it apart you'll see it's pretty simple mechanism, so once you know how the board attaches and you have the boat in a position to get at it, just start removing parts and you'll see there's not a lot to it. Just take notes/photos of how it all was before you took it apart. You can't really do much damage as long as you don't a) let the board drop or b) hit or pry anything hard enough to crack fiberglass. The biggest pain is working your way through old caulk, paint, and other fun surprises you tend to find in 40 year old boats. Do you have Roger Conrad's book? If not, and you're still at a loss, I highly recommend getting that book - I'm not sure anyone here could write anything more thorough.