1. "The smallest x in the world" is what is called a non-rigid designator. It has a reference, but that reference shifts. For example, "The current president of Poland has an identical twin" used to be true, but no longer is. "The current president of Poland" has an extension (what it points to) which is determined by its intension (what it refers to under particular conditions).
2. Jones's question is formed from a purely existential statement. It is not clear that this kind of statement is meaningful.