Was 1900 just a fictive person?

I just saw the movie for the first time and I'm glad I did.

A theory I have is whether 1900 existed at all. This is what Max actually says in the beginning of the movie several times, that he did not exist.

For example, how could 1900 hide that well in that old ship wreckle, without food, for such a long time? It makes no sense. By bringing the phonograph, Max found a way to revoke the fictive person inside his head once again and have a last conversation with him before the ship was blown up to pieces.

Another example: At the beginning of the movie, Max wondered where the shop owner found that record. He said he found it inside a piano cabinet. But in the final scenes of the movie, the shop owner asks Max who hid the record inside the piano cabinet. Max replied: "I did". How come? Did he find the pieces in the garbage bin where 1900 threw them? If yes, why did he hide them inside the piano cabinet? Likely, the piano is being tuned regularly and they should have been found then unless the piano was being abandoned. My theory is that the piano was Max's piano and the record was Max's own.