Quick question. I had read somewhere a while back as to what powers you can and can't use with each other. I need some current rules clarifications.

Charge and CCE?

Running Shot and RCE?

Thanks in advance.

Yup. Charge is a power action, CCe is a power action, they don't work together.
Same deal with RCE and Running shot.

The reason Charge and CCE do not work together is Charge says:
"Give this character a power action. Move this character up to half its speed value and then make one close combat action as a free action."

So the character can make one close combat action. However, CCE says:
"Give this character a power action."

Since Charge only allows you to give a close combat action not a power action you can not activate CCE.

The same goes for Running shot (which allows a Ranged Combat Action) and RCE (requires a power action).

And you can't give one power action that triggers them both since one action can only trigger one power at a time.