- Zero cars have driven by.
- Not one car has driven by.
Both of these sentences are fundamentally describing the same thing semantically and yet they demand different number agreement. Both of these are possible because grammatical number agreement is only partially informed by semantics.
Just because some descriptions of a lack of something have plural number agreement, that doesn't mean that all descriptions of a lack of something must have plural number agreement.
So, it is true that zero takes plural number agreement, and nobody takes singular number agreement. However, there is no reason that these have to work in the same way.
I have no idea what your second question (regarding TOEFL) could mean. Any can refer to singulars or plurals — it completely depends on what is in that blank space.
- Is there any water left? (Singular verb agreement for grammatically singular water)
- Are there any cookies left? (Plural verb agreement for grammatically plural cookies)