Thanks for your detailed pointer. Skimming the paper briefly -forgive me for not taking the time and effort to register and dive into the software if source is available- to me it looks as if the usage steps, not the underlying algorithms of the plugin are explained in the paper. In this case, I think other articles of (the lab of) professor Kutsuna are the best source for more information on the inner workings of the software.
On your second question: if you threshold a grey scale image for skeletonisation as a first step, it becomes binary. Then a standard skeletonisation can be performed. The radius of the bi-tangent circles on the page with explanation of skeletonisation principles you linked to may well be the result of the skeletonisation in the form of skeleton pixel values representing this radius. If a binary skeleton is needed, you could always simply threshold this resulting image, while if somehow the radii could be of use, it is a waste to ‘simplify’ them to binary by default and return the binary image.
I thought your question to be more involved in simplifying the skeleton, e.g. how do I reduce my skeleton-pixel-set to lists of coordinates of connected branching points, or something along that line.
Hope this answer helps. Thanks.