Correction on #3: It was generally the brakemen, not the engineers, who were doing the coupling. (Engineers mostly stayed in the engine.) It’s horrifying how cavalierly this problem was treated; there’s an old joke about how, at conventions for brakemen, everyone had to pair up to applaud.
Brakemen also had the unenviable job of running along the tops of the cars while the train was in motion, jumping the gaps to get to the brake wheels on each car. In fact, I’d argue that more important than the automatic coupler was the automatic continuous brake—particularly the Westhinghouse air brake and its gladhand connector, still used today on railways and semi-trailers—which was considerably safer (both for the brakemen and also for everyone else, since trains would now fail safe and stop if they broke) and made longer and faster trains possible.