Who can see my new DV website?

Only you, until you publish it. A website made with Create my website (Tools → Website & Booking → Your DV Website) starts private: visitors to its address see "This website isn't published yet", and search engines are told not to list it. You and your admins see the real site by pressing Preview my website or opening the editor. When it's ready, press Publish my website and it goes live for everyone; Unpublish makes it private again. A done-for-you site stays private until you approve it.