In the original, why does Hutter go to the trouble of the Bedsheet Ladder if Orlok had just left the castle?
It was implied that Orlok locked him in the castle to prevent his interference at some point after he discovered Orlok's resting place, and he was not tough enough to break down the door.
In Werner Herzog's remake, why did the sun kill Orlok/Dracula, but not the now-vampirized Jonathan?
It's only specified that sunlight will destroy a vampire if a woman of pure heart distracts it so that it doesn't notice the crowing of the first cock.
Actually it looked to me that the sun only paralyzed him, hence Van Helsing's "Hurry! Fetch me a stake and hammer!" after he entered the room.
Another problem with the Herzog version: Why did Jonathan turn into a vampire when all of Orlok's other victims simply died?
There can be a fine line where blood loss is concerned. I am assuming that Lucy's distraction from abroad and Dracula's departure thereafter prevented Jonathan from being dangerously drained, while others (Lucy herself included) were not so lucky (or maybe unlucky, if the same fate would have ended up befalling them had they survived.)
The Count offers Lucy a way to save Jonathan if she allows him her love; it may be that Dracula purposefully left Jonathan to live so he could use Jonathan's life as a bargaining chip, but to leave a victim of the bite alive is to damn them to vampirism.
Do you have nosferatu?
In the Herzog remake, why did Van Helsing and the others, after discovering that the ship was full of rats, leave the plank there for the rats to come out onto the land?
The rats probably would have swam across anyways, and panic likely left the most obvious form of possibly stopping The Plague furthest from their minds.