Secretary's statement that "singularities are only a theory" is true. This is because we can never actually see inside a black hole to find out if there is indeed a singularity- the event horizon cuts us off and prevents us from making any measurements or observations within the black hole itself. There could be pink elephants dancing around in there for all we know.

The black hole does not have an infinite mass, however. Since we can't measure anything inside the black hole, we have to instead infer its mass by the strength of its gravity. So, we make observations as to how strongly stars and gas are attracted to the black hole and then calculate the approximate mass of the black hole.

Regarding your second question: there is no direct evidence that has proven the existence of superstrings. Superstring theory is (I think) consistent with current observations, but there hasn't been any difinitive proof for the existence of superstrings. The primary reason for this is because strings are so very small. Since everything is made of strings, you can only observe strings with other strings, which are the same size. It's akin to trying to figure out the structure of a billiard ball when you're blindfolded and all you have is another billiard ball. (Only it's harder with strings.)