For me, both of the second possible meanings are correct and there is little or no ambiguity.
Your own explanation for the first sentence shows how to make the first possible meaning clear: add "even".
I don't know whether even two of them...
For the second sentence, the use of "some" in a negative sentence like this strongly indicates that the second possible meaning is the only natural one. If you wanted to make the first possible meaning clear, you would need to substitute "any" for "some" (as you already suggested):
I don't know whether any of them...
I hope this helps.
- For Teachers