To the Skirmish question, no it isn't multiplied. It is precision damage, which never gets multiplied.
As to timing, you're right that a charge normally takes a full-round action. Battle Jump, however, gives you a new condition under which you can execute a charge that is not tied to a specific action type. So long as you fall a certain distance, you trigger a charge. This is the whole principle behind the multipouncing builds: Move action to jumpounce, Standard action to jumpounce, and then if you use ToB Swift action for Sudden Leap to jumpounce a third time.
And yes, the distance you jump counts against your movement for that action. Thankfully, you can always choose to take a lower Jump check, so that you aren't stuck until next round.