Yes to 2) and 3), but I wouldn't overstate 1). The Sten Gun was no great marvel of precision engineering and yet it was enormously successful in certain roles. True, it had its issues; nevertheless the engineering of the 1850s and 1860s was well up to that standard at least (assuming someone got what would certainly have been a revolutionary idea). My family owns several firearms from that era, and there's some sweet and clean work in them. At the very least, the engineering skills and industry existed to produce some sort of automatic weapon, if the conceptual leap had occurred.
It's the steel and not so much the machining that is the issue here. While it might be possible to manufacture wrought-iron assault rifles their reliability would be low; too low for widespread military use. Mass production of steels did not really begin until the 1880s IOTL, so such weapons would be unlikely before then.
While I agree that manufacturing in the mid nineteenth century was often quite good and their products very well made they still don't measure up to later products. Compare a Colt revolver from 1850 to one from 1900; which has the better workmanship? The latter, right? Why? Because the materials available at the time were better for the purpose. Not just the materials in the weapon, but the materials in the tools and machinery used to make the weapon as well. Better tools mean closer tolerances and less variation, which permits the manufacture of more reliable and powerful weapons.
The mass manufacture of steels really was a game changer; it made mass production of automatic weapons, internal combustion engines, steam turbines, quick-firing artillery, submarines, skyscrapers, and a host of other items possible. It is impossible to overstate its importance.