Skill empowering
 

I was just wondering if when you empower a skill, it transfers to later skills you get in that series

eg: I put 5 points into empowering the cooldown on Aimed Shot[01]. When I get Aimed Shot[02], will it also have 5 points empowered in cooldown, or would I need to spend 5 additional points?

Yeah, empowerments applies to all levels of that particular skill, so you don't need to get another five points if you use the next one.