"What does a cow give us?"
I am just wondering if 'COW' is singular, shouldn't the sentence be
What does a cow GIVES us?
No, it shouldn't.
You're confused because it's a question, so the sentence structure is inverted. The uninverted sentence structure is as follows:
A cow does give us what?
The subject-verb isn't "cow give." The subject-verb is "cow does give." Based on the third-person singular subject "cow," the verb "do" is conjugated into the third-person singular present indicative tense "does."
In this sentence, "does" is a helping verb. When you have a helping verb, the structure is: the helping verb followed by the main verb, which appears in its infinitive form but without "to." Since the main verb is "give" and the infinitive form of "give" is "to give," you would write "cow does give," not "cow does gives."
So, when you return to the inverted structure to form the question, nothing changes as far as the verb is concerned, so the proper way to write it is:
What does a cow give us?
This is a SVA (subject-verb agreement) matter. Normally, you'd be right if the subject was singular. For instance, "He (singular subject) gives (singular verb) good advice (object)" is a grammatically correct sentence because the verb agrees with the subject. However, in your sentence "What does a gow give us?" the subject isn't "cow" but "what." At first glance, you'd say the cow is what's giving, but actually "what" is what's being given. If you had asked, "The cow gives us what?" then you can see how "gives" makes sense; the cow is the subject because it is giving something, albeit something so far unidentified. In your sentence, though, the answer to the question won't necessarily be milk or meat or leather. The answer is, quite plainly, what. What is what's being given.
PS: This probably sounds really nonsensical. If someone could add to my answer to clarify, it would be appreciated.