Say I've got a cluster missile and already have a tl on my target, can I use marksmanship to modify both attacks on the missile, or is it just the first?

Both. This is one of the very few good uses of Marksmanship, aside from interactions with Gunner. (Han Shoots First builds being the classic example).

Edit: It works particularly well on Vader since he can TL + Marksmanship as his 2 actions.

It last until the end of the turn.

That's what I thought, thanks

Both. This is one of the very few good uses of Marksmanship, aside from interactions with Gunner. (Han Shoots First builds being the classic example).

Edit: It works particularly well on Vader since he can TL + Marksmanship as his 2 actions.

That's the only way I fly Vader, but I give him Concussion Missiles to ensure hits.