We are not sure how this card should be played. When the attempt is made again are all of the skills used from the first attempt?

After you complete a mission, it either is discarded or returns to your hand.

So contingency plan, you could play Build Alliance, then it returns to your hand, then you could play contingency plan with say, Mon Mothma or Admiral Ackbar to play Build Alliance again from hand.

All Contingency Plan does is assign you to a new starting Mission from hand. You don't resolve the new Mission in the same Leader Action. And you just resolve the new Mission as you would any Mission.

It says, "starting mission". So isn't that Leader's assignment limited to the 4 original missions you begin with?

It says, "starting mission". So isn't that Leader's assignment limited to the 4 original missions you begin with?

Yes, the ones with the little yellow arrows at the bottom.

So you can play Build Alliance (for example) twice in a turn, once with the initially allocated leader and the second time with the leader(s) allocated to Contingency Plan

So you can play Build Alliance (for example) twice in a turn, once with the initially allocated leader and the second time with the leader(s) allocated to Contingency Plan

yes.