Are there undiscovered elements?

Answer 1

Undoubtedly! When I was in school (not really THAT long ago), there were only 105 elements known, now there are 116+

Answer 2

This is a hypothetical, and so the answer will also be hypothetical. Yes, it is possible that other undiscovered elements exist somewhere in the universe (or outside of what we know as the universe). Some new elements have been synthesized, and based on what chemists/physicists know about elements, it can be predicted what any new element would behave like and predict it's properties. Stability would be a problem, as those elements with higher atomic numbers tend to be remarkably unstable.