This set confuses me. On the one hand, all the cards except for Force shield, are pretty neat. On the other, the troopers are crazy expensive and rather aggressive, which means they don't really fit into Sith's usual control-style decks. The events seem to be far less useful in splash decks than in mono-Sith. Has anyone found a good place for this one? Because I can't.

Don't think it so much. The troopers are risky investments, but big threats on offense and defense. The events can give your objectives a bit more staying power, and The Second Phase helps play your big mains earlier. Decent 1x in Sith.

It's not particularly synergistic with any faction, but it has enough internal synergy to work by itself.

I'm gonna try it again with Yularen. The extra repairing on his pod could work pretty well here.

The units are actually really good on defense. With an edge battle won, they have the magic 3 damage to kill a Jedi main or RSXW. 

I once went to a tournament with it (as a one-of obviously) and it did pretty well, but there are better options. Definitely playable though. I think I once went T1 Vader and T2 Palpatine back in the day (without sacrificing T3). Not thàt big of a deal, but fun nontheless.

Keep in mind that - in the endgame - the troopers are actually affordable. When LS was slower, this was a real option in control (that wants to stay alive). That being said, it does add some protection too. If the rest of your sets are full of great cards, it doesn't hurt that there's one trashcard amongst these. The fact that the other 2 are conditional when you aren't playing mono-sith makes it narrow in use.

How does the synergy between the Objective and the unit work exactly? Is damaging the objective by triggering its Action separate from the Interrupt on the Dark Trooper Legion unit? i.e: if you choose to trigger both, does triggering the unit's Interrupt cause an additional damage to the objective (assuming you chose to damage The Second Phase to reduce the cost), or is that damage already counted in the Objective's Action?

Basically, is it a two-for-one (reduce the cost by two, damaging TSP only once), or is it just a more risky way of reducing the unit's cost twice? As far as I understand they're two mechanics triggering separately, but we've had some uncertainty about this at our game table.

They trigger separately.

So you could first use this action, then attempt to play a DT Legion and use it's interrupt on all your objectives, dealing a total of 4 damage (2 to The Second Phase, 1 to each other objective) to play the Legion for 2 resources.

If the LS played a mission, you can damage it at well with the interrupt to get a bigger discount.