Re: To space, or not to space? That is the question.
If the division board is being used as a follower board to just reduce the amount of combs for the mating nuc, then leave bee space. If you are dividing the box to make a double mating nuc in a single box, then leave no beespace. However, always leave bee space between the bottom bars of the frames and the bottom board as bees will travel from comb to comb using the beespace on the bottom. I use 3/4" beespace on the bottom board myself, mostly for construction reasons... 1 x lumber and plywood comes 3/4" thick.
20+ years, raise my own queens, feed when needed. I treat, but have not perfected varroa management yet.