You have to use the "Other App" at the bottom of the right click menu before Windows will add it the list of programs that can open the file. There are many other ways of creating the association but that's the easiest.
With V10 the version number is now appended to VCarve so where it used to say VCarve in a menu like that it now says VCarve 10 so Windows treats it as a completely different program.
You can drag and drop PDF files into a VCarve session or open them directly from within VCarve as well as importing them.
PDF is not a default association for VCarve. Re-installing won't do anything as it's all to do with Windows. Prior to this release if you had two versions of VCarve installed (say V8 and V9) and you had set them up to open PDF's then you would have seen VCarve in the list twice with no idea which was V8 and which was V9. Now once you've set it up you should be seeing VCarve 10.
The default locations for Open and Save dialogs is now set via an option on the Options dialog in the Edit menu. You can have it set to Global (use last location), Job (use the location where the job was loaded), Operation (last used for that operation so you can have different locations for toolpaths and vector exports for example).