My opinion (not a professional language teacher, and this may be more subtle):
"work from" and "work at" mean almost the same thing and you will not cause confusion or communicate something wrong by using the wrong one.
I think that when I "work from" the underlying metaphor is that I am SENDING work FROM the place that I am "working from" TO the place that I "work for." So, for instance, "I am a speechwriter in DC. My boss lives downtown, but most days I work from home because I hate the commute."
compare:
"My job is to cook breakfast for the 500 people who live in my building, so I work at home!"
But I don't think I would notice if in either of those sentence you swapped the from and the at.
As for at and in, that's hairier. "I work in home" is definitely wrong. "I work in my home" is not wrong but is weird. "I work at home" is much more natural. This is probably the specific semantics of the word home, and has nothing to do with working. For example, "I work in a studio" and "I work at a studio" mean virtually the same thing.
Prepositions don't have to be part of a phrasal verb, in fact I would say most aren't. In this case, none of the prepositions have any special relation to the verb. They're all literal descriptors of the positions the subject goes through during the action.
Try to break up the sentence into the smallest chunks that make sense. Here: He fell. Yeah, that makes sense, that's true. Okay, where did he fall? Into the pool. What did he fall off of? He fell off the ledge. So now, put it together.
He fell off the ledge and into the pool.
You can leave out the "and" here, but it's still there for grammatical purposes. You can tell if you use three prepositions:
He fell off the ledge, through the air, and into the pool.
You can't leave out the "and" here, there's no way to use three prepositions without the conjunction. That means that there's no way to do it with two, either, and the "and" is still there, it's just not spoken.
Right and straight are both intensifiers, and don't really make sense to me here. There's not exactly an indirect way to fall off a ledge and into a pool.
I hope this helps.
Edit: A note to help distinguish between phrasal verbs and normal prepositional adverb phrases: phrasal verbs don't accept objects of the preposition, and they don't pair with prepositions in conjunction phrases.
The roof fell in. good
The roof fell in the house. not good
The roof fell in and onto the ground. not good
The roof fell in onto the ground. good
Does that help you see the difference a little better?
Best Answer
I would say hang the bag on the hook, the broken wing was hanging off the aeroplane, the light fitting was hanging from the ceiling and HANG ON FOR DEAR LIFE!, so I suppose that your examples are not really interchangeable after all :)