1 Can I play an action card after I finished my 5 action points according to the rule that I can play an action card when I want for a cost of 0 action points???
Yes, on your turn you can play an action card even after using your action points.
2 Action card "move one of your knights past one other knight by jumping over it.....": the knight that I can jump must belong to an opponent or it could be also a my knight? Can I jump the king?
You can jump over any knight regardless of who it belongs to. You cannot jump over the king.