I'd like to know if there is a reason why Dickons and Edison chose exactly 35mm as the width of their films.
Yes, they took normal 70mm film stock used to make movies, and cut it in half. It was cheap. It was really not a big deal at the time.
There is a history of the film formats and sizes on this site. It goes into some of the particulars you're interested in. It boils down to the size being half the size of film (70mm) of the time.