First off, I'd start with the July '61 campaign if you're playing the South. After you figure out the mechanics a bit, then go for the April one. It's significantly tougher for the CSA starting in April because of quite a few factors.
Not sure about the Kentucky thing, I meant to ask about it, but completely forgot. In real life, the US sent troops in, then quickly recalled them, the CS sent in troops about the same time, but they stayed. Both sides claimed the other side started it, so it might be a set event, not sure. I know it doesn't always join the Union though, as a matter of fact, I've never seen them join the US.
Any troops not led by generals will be active, unless locked. So they'll be able to move, but should fight with a significant penalty. Even inactive generals can move their troops, though they will do so slower, and are limited to the defensive and passive postures.