You can just have your HUD ask the player for all running Abilities when it updates. That’s how I would do it. That way the HUD is just reading from the player, it doesn’t require any cross communication.
Yea, Abilities will run on whatever, as long as they have an Ability Component. If you are using a common interface for variables, then that code would only work on objects that inherit from that interface. But, to Able, it doesn’t make a difference.