For the issue with Stress and Devil’s Bargains, it sounds like he isn’t hard enough with his Consequences and/or is too giving with Position and Effect. If the players don’t want to expend their Stress or take Devil’s Bargains, then there must be very little danger. He might make Clocks shorter so their effects are felt sooner, increase Consequences or just reassess Position and Effect to make the world a bit more dire. It’s also important to communicate that Stress is not HP — there’s a Harm track for that. Stress is a tool for the players to help game the system, actually, and mess with the mechanics that the GM is bound by. Devil’s Bargains are a way to keep the narrative dynamic and shifting and helps the GM move the levers on the world in the background (sometimes bringing those effects to the foreground, esp. when there are Clocks involved).
For Engagements outside of the Crew’s league, let them do it. Firstly, the Crew should decide on Engagements together and then, if they all agree to assassinate the emperor, let them. They may need to do some missions first to get the fictional positioning for that to make sense in the narrative and to be mechanically able to assassinate an emperor, but there’s no reason they can’t. It sounds like he and his players need a refresher on Tier and how that affects the mechanics of the game. And I really would suggest taking that request and breaking it down into smaller missions that add up to an assassination (which may, correctly, take many sessions).
For the Hunt Action, I agree with clarifying situations where that Action doesn’t make sense, but, in the end, players get to decide which Action they’re rolling. The only recourse, really, he has is to make the Position/Effect Desperate/Limited; that’s the clearest way to communicate the inappropriateness of the Action — even on a critical, they hardly accomplish anything with Limited Effect (and that would probably encourage them to take Stress or a Devil’s Bargain in order to increase Effect…)
ETA: extra emphasis on zero effect! I forgot about it during my response!