Question: I've noticed that every episode has scenes where the camera is swaying a little, suggesting the camera was handheld or resting on the cameraman's shoulder. Is there a reason for filming this way, instead of just using a steadicam? It doesn't really add any sense of style to the show.
Answer: It is a style of filming a scene, a style of camerawork. In your opinion it doesn't add anything, but they do it for that purpose.
Dead Freight - S5-E5
Question: How did the train conductors not hear the water pump Walt was using to pump water into the tanker? They were only around 800 feet away in open land, so it should have been audible.
Answer: For one thing the engine running the pump isn't that loud. The characters have conversations at a normal volume without having to scream at each other. Even if the conductors could hear it, there is no reason they should care or be suspicious. It just sounds like an engine running in the distance and they don't care enough to look for what is making the noise. At that very moment there is also a kid riding a dirt bike in the area. Engine noises are a very common thing.
Question: Would Gus not die instantly from his injuries of that explosion? Instead, he has time to walk out, straighten his tie, traumatize the nurses, then die? Or is that all for the sake of good TV?
Answer: Definitely just for the sake of good TV; in reality, this would be instant death (or at least, very soon after, and no way one could just get up and walk). There's a featurette on the production of this scene, and Vince Gilligan addresses the liberties taken with reality here. He felt that since Gus was such an iconic character, he deserved an equally iconic death, hence the calm, cool, collected way he walks out of the room with half a face. Gilligan said he also wanted to briefly fake the audience out, as we see Gus walk out from his "unaffected" side first and assume he somehow survived the blast.
Question: Were the interior scenes in Walter's house actually shot inside that house or at another location? The view down the hallway towards their bedroom doesn't seem to fit the size of the house, which from the front looks much smaller.
Question: What was the purpose of the flashback at the start?
Answer: As the other answer indicated, it is a common filming technique used to achieve various visual effects. Handheld cameras can create a deliberate sense of movement that follows a movie's action. A cameraperson can physically move in much closer to an actor, creating a more intimate connection between the character and the audience. It can also reflect a character's movement from their vantage point, and can be used to create a greater sense of realism with an edgier, less-rehearsed, or a documentary-style feel.
raywest ★