How are paper ketchup cups made? How are they formed and specifically
how are the edges rolled over?

I haven't found anything, but the common term for the product is:
"paper souffle cups."

Apparently the main manufacturer of these cups is Sweetheart. I
haven't found details on how they are manufactured. As blader-ga has
pointed out, they are often called "paper souffle cups." Other terms
I've seen are "pleated paper cups" and "condiment cups."

Apparently, the technology for making the pleated cups themselves is
sufficiently old that the patents are not available online. (The
patents would reveal the process for forming the cups themselves.)
There is some information online about the manner in which the rolled
upper edge is formed for other types of cup (e.g., standard paper
drinking cups).