1. I love militia, and I hate them. Militia are by far the most cost-effective infantry, not only in resources but also time. As a Federal player I can and do build tons of them, brigade them, and train them to regulars with the several training generals. I use them almost exclusively to garrison all those disloyal cities, but the opportunity for exploitation is all too apparent.
Historically, I have a hard time figuring out just what they are supposed to represent. Almost the entirety of both armies were volunteer regiments raised to fight the war, with no other purpose. Units made up of pre-existing state militias probably had a small advantage at the outset of the war, until training the rest caught up. My guess is that they are meant to represent home guard units never sworn into federal service, especially in the model of the many units in the several iterations of Missouri militia (although these were often mounted).
I think the best fix for militia is to prevent them from upgrading, and perhaps to stop brigading them from affecting the force pool (as it is currently, brigading seems to effectively double a state's force pool). Elements recruited for maneuver combat should almost universally start as "conscripts." Alternatively, there could be an "interior" option to call up a state's (fixed) militia units for a 3-6-12 month period.
2. Combined-arms brigades are ahistorical, and probably contribute to artillery over abundance. A few combined arms "legions" were formed in '61, but these were typically regiment-sized and broken up into their components by mid '62. Brigading infantry with artillery lasted a little longer, but generally artillery was moved from the brigade to division (or higher) command level. Even infantry brigades were rarely recruited together (especially on the Federal side); rather, each state recruited individual regiments, and these were parceled out to areas of need, for later brigading with units often from a variety of places. My recommendation would be to allow the recruiting of single-arm units only, but allow formation of "brigades" (basically divisions with a cost of 3 CP and max of 5-7 units) from the start of the war.
3. The current force pool structure allows one to recruit exclusively from a single state or region, which again is highly ahistorical. For instance, it is often disadvantageous to recruit from places like Maine, Michigan, and Minnesota. Paerhaps a better solution would be to have each state's force pools expand slowly over time, forcing the player to accept volunteers from throughout the country (if they wish to use their full recruiting potential)