It's a question word that can be used whenever there are two options (in this case "yes" or "no"). But it's a little bit formal, so not always used in speech.
Why not? בינינו might be more accurate, but I think one would also use בתוכנו in such a context
I disagree. בתוכנו in this context is really wrong, unless (for example) the alien is literally located inside the human body (like in the movies "alien", "host" etc).