Basically these two majors have nothing to do with each other. But probably that would be individual, I mean not necessarily every engineer could be a writer, or opposite. These two jobs are not connected but anyhow but it's up to individual if they desired it or loved to follow both.
Not really and so they have what's called Tech writers who write for Engineers. So Manuals and directions are usually written by these Tech Writers working closely with Engineers. Now there are exceptions to every rule but in this case are pretty rare
Really, what job someone does has nothing to do with writing. Writing is a gift that an individual is blessed with. You could be an engineer and be a great writer, or you could be a hobo and be a good writer. It is purely how your brain is wired.
Some are, some aren't.
Engineers tend to be concrete thinkers; writers tend to be abstract thinkers. (And this is a technical distinction--neither proclivity is better than the other---Google the concept.)
"Generally speaking," engineers work with things a symbols to manipulate reality. Writers work more with words.
Both can be equally intelligent, but may have different individual skills.