you need to create an account and save the pen to your account- to copy the pen with the test suite to your account and work in that, use the fork button in the bottom right corner
try to right click on an image and open it on a new tab - when you can open just the image in the url bar of the browser there will be the image url, most often ending in jpg or png
you can build the projects on your computer but you can’t use drive, you need a live version of your project with the code also publicly viewable
From the FAQ:
Do I have to use CodePen for the front end projects?
As long as your code is publicly viewable, and you have a live demo, you can use whatever you want.
You can use GitHub pages or surge.sh as alternatives to CodePen.