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."
"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.