The server is needed for serving responses to api calls when the user navigates pages.
If you don't have server, you won't be able to have a SPA, but just a static generated website.
Exactly, so it's not isomorphic. An isomorphic application wouldn't depend on its inverse to work.
Isomorphic means corresponding or similar in form and relations, not independently of each other.
If it's not independently of each other, it's entirely unclear what the value of the phrase IS. It, again, seems to be reduced to shared logic—a cross-platform library.