Like it says, can new sonar open Guitar Tracks Pro 3 projects?  And...... Bonus question: Does anyone know if GTP3 will run on windows 8.1?

I am pretty sure it won't - I think I tried a GT4Pro project in Sonar Platinum.  However, if you have the audio, you can import it into Sonar and work with it.  Of course all of your plug-ins and settings will have to be re-created.

What is the extension for GT4 Pro? 

I think its .gt4 or something like that.  I am pretty sure its not .cwp.

When I worked in GTP the extension was .wrk which was the same for Home Studio, I believe. I think I had just the first two versions of Guitar Tracks, but a quick test for the OP would be to simply open one in X1 if loaded on his machine (IIRC from the other post made). Cakewalk has been good with both forward and backward compatibility (forward loses plugs, and backwards may lose both plugs and new features).

Hmmm. Just a thought, I'll give it a try, but perhaps in any case it might open bundle files from any version?

Well, I may have been wrong - looking at my laptop, where I am pretty sure I have not opened any of my really old projects, and they are all showing as affiliated with Sonar X3.  Although these were back ups as I never had GTPro4 on my laptop.
 
It looks like the project will open and the tracks and buses will be there.  Not sure if earlier versions of GT will do the same thing but its probably worth a try.

Bundle files open as well. The old extension was .bun an SONAR still recognizes them.

As far as your second question, I found my old copy of GT Studio several months ago and IIRC, the installer would not run even when setting compatibility all the way back to Win95. It would, however run in "Windows XP Mode" which is an embedded instance of XP included with Vitas/Win 7. However, I believe that was removed from Win 8/8.1.
 
In all honesty, if you have X1 (per your other post), I would start by re-installing that and getting the patches to get it to X1d. X1d was stable, and the "skylight interface" (which you didn't like) didn't "go away." Even if you get GTP to run and jump into Artist, you will still have the same "culture shock" as before. It is a better mindset to start fresh and learn the software for "what it is." The new SONAR has a ton more features and capabilities than Guitar Tracks.