During the Resource Phase do I have to split the Resources evenly?
No! Feel free to divide them however you desire! You can even split them into a pile of 0 cards and a pile of all the cards (of course, you’ll be stuck with the pile of no cards). If you can make one pile have fewer resources, but the resources your opponent needs, then you can come out ahead!
I want to use the ability on the Capital card in my hand, but I don’t want to discard it.
You’re in luck! Using the ability on a Resource card during the Ability Phase doesn’t cause you to discard it. You can have your cake and eat it too! (Or in this case, you can use your Capital card to draw an extra Resource, and then use the Capital card to complete a Milestone)
My Target Populations’ care icons match those on the Improvements I was dealt—do I win?
Not unless you’ve completed all the Milestones on top of those Improvements! Once you have removed all the Milestones from on top of the Improvements that match the Target Population cards you can discard those Improvements to meet the needs of that Target Population. Only once you’ve met the needs of 2 Target Population cards is the game over!