1) You can see in the first of my images that there is about 3/16" of wood on each side of the barrel. I wouldn't slim it down much further before cutting the rod groove - can't see any advantage.
2) Use wooden blocks to guide the drill. For a half stock, I use the pipes already hard soldered to the rib and the rib soft soldered to the barrel, to guide the drill . This gives you a rod hole that is the same size as the holes through the pipes. Usually the forend of a half stock is beefier than on a longrifle, so that's ok. On longrifles, I usually drill the rod hole 1/16" smaller than the rod groove, so that it will receive a tapered rod, and minimize the depth of the forend.
3) 3/16" of web is maximum, IMHO. I shoot for 1/8" - 5/32" for the web.
4) Definitely leave the barrel in the channel when drilling the rod hole. I don't think this requires an explanation. I don't normally drill "check holes' until after the hole is drilled, and it is just to satisfy myself that all have gone as planned. Other's may have more to say about that.