Can I see the screenname of the contributor who created an entry? Or is this private?

It's kept private.

This is displayed for some items including reviews and biographies, unless the writer chooses to be anonymous; for most of the other data, it's probably impractical because many items such as trivia, goofs and movie connections get revised or edited by multiple users. (One user might submit a movie connection, while another may later add an explanation.) If you're talking about who may have submitted a new title, keep in mind that some titles are submitted by multiple people at once; other titles might have been initially submitted by one contributor with just the bare minimum of information to get approved, while other contributors may have later submitted the bulk of the material on the title.