Did not use template or jig. Just freehanded and eyeballed to get shape. I am far from an expert on woodturning.
No standard height. One is 58 3/4”, 2nd is 39 1/4”, 3rd is 61”
The one tha is 39 1/4” is mounted under my radial arm saw table. All others are below existing cabinets.
Balls are glued to dowels. Before gluing, I made sure that they would pass through the tube of paper towels. Also, in this design the dowel lays in the cradle. You can remove the empty rod from the front. You are correct to be sure there is appropriate room to use and replace towels.