How do I convert shape borders to paths in Photoshop CS5?
How I have tried: I have searched through the tools in the program and search through forums and the Adobe help site on the web.
Select the shape path by using the Path Selection tool
Once selected, copy the path with Ctrl/Cmd-C.
You've now copied a path. Pasting this onto a shape layer will turn it back into a "shape", but pasting into a non-shape layer will just leave you with a path.
I don't have a "border size" anywhere in Blending options, but you are right, layer styles do not scale when transforming shape layers.
You have to scale the shape, then scale the layer styles separately.
You can't easily set any layer style aspect as vector data. If you want layer styles to scale with the layer, convert the layer to a Smart Object before scaling it.
Photoshop CS6 and newer made this easier with Vector layers as opposed to CS5s Shape layers. Vector layers allow for a stroke setting which is vector based and more easily scaled.