Just two questions:

If the LS plays Trench Run and the DS has no enhancement-killing cards, then (theoretically) there's no way the DS can win?

If the LS plays Trench Run if the Death Star dial is at 11, does the LS automatically win?

I've thought about it and this was my theory:

As soon as Trench Run is applied to the Death Star Dial (DSD), Trench Run itself becomes an objective like The Heart of the Empire objective (10 damage and LS wins the game). Trench Run does not change the DSD into a damage dial, else the card will just be overpowered; LS could just slap the card down when the DSD is at 11 and win the game.

Thematically, this makes more sense. It wasn't easy to make a trench run, but it was possible hence the 10 damage capability. It also makes sense that it can only be engaged during the Conflict phase ("You may engage the DSD as though it were a DS objective") since it was that way in the movie.

I...think this is how the card works.

The dial is not used to track the damage. Just use normal damage counters. The dial being at 11 has no bearing on Trench Run. It's unlikely LS can do 10 damage to the dial before dial hits 12 on next DS turn.

Understood, but it's easy to misunderstand the card text to think that the DSD is a damage counter.

In addition to Toqtamish's clarification for you, I will add that Trench run is a very big gamble of a card. If you don't get it on turn 1 or 2 there's not much of a point to play it out. Alternatively, suppose that you do play Trench Run on your first turn. You are now signaling to your opponent that you are ignoring his Objectives and making attacks only on the Death Star Dial. This limits your options considerably and makes it that much easier for the Dark Side player to successfully defend. In my experience, that card is best left to an edge battle for its 2 Force Icons. The Rebels are not too good at winning Edge Battles so the better option to play a Rebel themed deck is to play out multiple Units and Engage each Objective once on your turn. Your opponent probably won't have enough units to defend with for every Engagement and you will eventually blow his Objectives to bits.

this card is undervalued at times. yes, it's not always your best option, but it can be great.

My best game was first turn Home One, Trench Run.

If you can keep the capital ship alive, or play it again later, it doesn't matter if they successfully defend, Home One's ability slowly takes out their other objectives as a back-up anyway.