Did the Civil War cause such a shortage that there was a demand for that much extra beef, or was it a change in diet, a new taste?
Chicago, Omaha and KC were all famous for their feed lots; was the cattle fattened there and then sent east to be slaughtered, or were carcasses shipped, and if so how did that work with out cooling cars? Or was it all canned in the midwest?
I've seen longhorns and even I can tell that their meat is very lean and tough; how did people cook that meat, was it all turned into some kind of pastrami or other deli meat? Or were even the tenderloins braised for long times? Or did people then grill steaks and just chew it longer?
I can't attempt to answer all your questions but I will try to address some.
Why did the drives stop? Mainly because of the expansion of the railway network. Initially cattle drives went a lot further north, probably all the way to the north east which was the biggest market for consumption. But when the railways started appearing things changed and the drives started centering on places like Abilene in Kansas. Cowboys would drive their herds there where the cattle would be purchased and loaded live onto the trains to head back to New York and other places. They would have been slaughtered and butchered in the east either at or much closer to their final destination.
As railway networks extended further, the need for cattle drives disappeared.
You should read The American West by Dee Brown. A third of the book is devoted to precisely this subject over precisely your chosen time period and its an excellent read.