how obtuse are the puzzles
There is only one type of puzzle in the entire game.
The game works by viewing "snapshots" of moments in time where someone dies (sometimes multiple people in a single scene). You need to identify who the victim is and what killed them. The game will confirm correct guesses in sets of three.
The cause of death is often obvious (but not always). To figure out the identity you need to piece together clues both from within the scene where the person dies, and also from other details. These other details usually revolve around finding the same person in another scene (the game gives you tools to track every scene a character appears in) and checking out where on the ship they work, where they sleep, who they tend to follow around, lines of dialogue, and so on. Other details like clothing and ethnicity can also be used to infer someone's identity.
It works really well. There are only a few identities in the game that I felt were particularly obtuse, and this was mostly from having to go back and forth between a certain scene several times to identify every person in it when the walk speed is so slow (every scene has a part of the ship that you need to travel to in order to enter).
If all else fails, there's no penalty for guessing and checking either. For example, if you're sure about two identities and three fates, you can just work your way down the ship's manifest until that third person lands you a "hit". I recommend not doing this unless you're stuck though. The game will assign a difficulty rating to each crew member (by face, not by name), and will also indicate if you don't have enough evidence yet to identify a person without guessing.