What is the “Quick Timer”?

Does GoCube-X and Rubik's Connected use the same app?

No, each cube has it's own App

Is there a tutorial in the App?

Of course! There is Onboarding screen once you first log into the App. There is also a tutorial section in the App to guide you on how to solve the cube.

Am I required to connect my Facebook Account?

You can signup using only your email address. Linking your Facebook account is not required.

Is there an API?

No