Singular vs Plural – One or More [Plural or Singular]?

The correct use changes depending on the sentence:

Do you have any idea how to do this?
Do you have any idea what to do?
Do you have any ideas for me?
Do you have any ideas for how to do this?

It seems that, if the singular or plural noun (idea) is directly connected by a subordinating conjuction (how / what / where / which / that), you use the singular; if it's modified by a prepositional phrase (for...) or by nothing at all, you use the plural.

Without using all that grammar jargon, I'd say use the singular if it's followed by how, what, that, who, whom, whose, which, etc, and use the plural otherwise.

To my (American) ear, "What would most people know about insulin?" is correct, and "What would most people knows about insulin?" is incorrect.

"What would the most people know about insulin?" sounds unnatural. "The most people" is usually used as a superlative, not as a way of referring to a specific group of "most people". "Most people" is deliberately vague as to which people are in the group, so a non-superlative use of "the most people" is usually self-contradictory.

"What is the most people you have ever talked to at the same time?" does sound natural. Notice that this question asks for a superlative -- the result of comparing the sizes of all of the groups of people "you have ever talked to" -- so this use of "the most people" refers to a single group of people. "What is the largest audience you have ever spoken to?" and "What is the largest group of people you have ever talked to?" sound even more natural.

"The most people I have ever talked to was 2,500 people, during a meeting at Town Hall." In this usage, "the most people" is singular.