Picked up the core set, a tie advanced, and an e-wing last week and have been having a blast. For clarification: since an unspent target lock remains after end phase, does that clear up a available action for the ship? For example, if Vader target locks Luke and doesn't use it that turn will he still be able to take 2 actions the following turn and still have target lock?

Also, how is running into the edge of play area resolved?

yes you get to keep the lock and perform your action the next turn (or in vaders case 2 actions)

whenever a ship would finish its move and part or all of the ship base is off the edge of the playing area the ship is removed from the game. note that the maneuver template may exit the area so long as the final position of the ship at the end of its move is wholly within the playing area.

Your target locks will stay in play until you use them to launch a missile or torpedo, or you use it to make a reroll. If you have a target lock on a ship and want to target lock a different ship, you just perform the target lock action in the Activation phase and choose the new ship.

Also, be aware that while Vader can do 2 actions, no ship is allowed to perform the same action twice in a game turn. And in case you were wondering, there are upgrades out there that allow other pilots to perform more than 1 action per round as well.

A helpful hint for future expansion purchases: When you can, buy a TIE fighter and/or X-wing expansion when you get a chance as there are different pilots and upgrades in those packs that aren't in the core set.