I am really bad at explaining things like this but I will try.

delegate is basically a way to lend your hive power to someone else. Power down is process that turns your hive power to normal hive. If I remember right powering down your entire account would take 13 weeks. Power down is something you would do once you would want to sell/ cash out part or entirety of your hive power. Rewards that you get on hive and splintertalks are different. in splintertalks you get reward that is related to splinterlands. Sorry if my explanation is not very clear. I would suggest asking @tarazkp. He is very knowledgeable about hive world and could explain most things way better than I could.