Tested with CC 2020;
One other way to export all resources as files is to export document as SVG. This is not keeping the original file names of course but exports all images as PNGs. Also note that exporting PNGs can take long depending on the image dimensions.
File > Scripts > SaveDocsAsSVG
You have a possibility to get strokes which have same lengths and directions as the curves in the mesh. Use the mesh to envelope distort actual strokes. Generally you will not get exactly the same strokes as the curves in the mesh, but they can be near enough. An example:
In the left there's a mesh which was originally rectangular but it is mangled a little ...
You can't apply strokes to inner mesh paths. They aren't actually paths. And there's nothing you can do to "expand" or otherwise turn them into paths. They are data constructs. You'll have to find another way to achieve what you want.
Your best bet is to probably to take a screenshot of the highlighted mesh (because the inner lines only show when the mesh ...