Thanks for asking and apologies for the problems you are facing with templates and theme.
As you don't see any templates in the list option, I suggest you to first update X and Cornerstone to the latest version. I see that you are using X theme version 6.0.4 and Cornerstone 3.0.4. I suggest you to update to the lastest release and see how it goes.
Here is the update guide that you can take a look: