I can only speak to KD, and a little on Carowinds:
1. Yeah, a full open-to-close day at each park should be sufficient, provided you don't want to do the water parks and you're going on a weekday. I see you're going in April, so water parks will not be a concern.
2. No downside to waiting to buy Fast Lane at either Cedar Fair park; I've never seen them sell out outside of the Haunt season. Probably won't be needed if you're going on a weekday.
3. As you can tell, weekdays will be comparably dead compared to weekends. KD is still on weekend only operations in mid-April, and so is Carowinds, so that might not be an option for you. Unless you're going during one of their spring break weeks (which are different), then yeah it could be packed.
4. Most people will tell you spend the extra day at BGW, but I'm going to say KD, especially if you value thrills over theming. Intimidator and Twisted Timbers blow pretty much everything at BGW out of the water.