First, thanks for watching!
My decision to put five artillery in each division is a bit of a guess on my part, since I'm not intimate with how battles work. I really should read up on "frontage." But I do understand that five arty can all be engaged in the same battle, although sometimes (often?) not all five can engage. So I guess I use five arty for three reasons, all of which might be wrong. 1) I have the notion that, in most battles, arty does most of the damage. So I figure I should add that extra arty. 2) Different arty types have different strengths. I give each division 1 "heavy" (like a 20lb), 2 12lbers, and 2 10bers, in the hopes that my generals have the smarts to use them in the appropriate situations. So I'm giving my generals flexibility. 3) It feels like 10 infantry is enough to protect the arty, while the arty do the damage.
As for your question about the militia in DC, I'm guessing you're referring to the state militias I gathered in Washington and St Louis in 1861? Those were for defense purposes, and to put under macclellan and halleck for training purposes. I think I understand that the "training" trait on those generals is to turn infantry(conscript) into regular infantry, which doesn't do anything to militia...but militia turns into infantry pretty quickly. So, I let those guys train there, then added them to divisions in 1862. I could easily be getting this wrong, and I'm certain that I could be working more efficiently here. But that was my logic, anyways.
Why do I put militia into divisions? I figure, why not? They're cheap, they turn into regulars eventually, and it doesn't seem to hurt anything so long as the division has a bunch of regulars and not too many militia. But it depends on whether I think a division will go into battle soon. For instance, the division I sent to Ft Monroe -- I figured the chances of it being assaulted were slim, so I didn't mind having a lot of militia in that one.
Does this answer your questions? I'm sure I could be doing all this stuff better, but for what it's worth, this is my thinking.