I have asked similar questions here before, but this issue still confuses me.
Yes, I remember seeing and even answering similar questions recently.
what's the difference between singular and plural nouns
"any" can be used with singular o plural nouns. In questions like the ones you propose, it all depends on what you expect as an answer:
1. If the exam is very difficult, you might use the singular to suggest that not more than one student -- if any -- may have passed it. The plural might be used to suggest that more than one student may have succeeded.
2. If this boy is really fast, you might use the singular ("any woman") to indicate that only one woman -- if any -- could run faster. With "any women," the question is more open: there may be more than one woman who can run faster.