You are correct, and for the correct reason. The subject of the sentence is "example", while our object is "expiration labels". The verb should agree with the subject, not the object. A much clearer example is:
"He sees many cats."
"See" must agree with "he" not "cats". This simple intuition is just more difficult to apply when using "be" because we want the two sides to be equal.
As for your last sub-question, "the" is grammatical, but not needed. "The" can be used for both singular and plural cases. For example:
I see children outside.
I see the children outside.
Both are correct, but with slightly different meaning. The first is children in general (I probably don't know these children), while the second is a specific group of children (a group that we understand from context).
In the case of your example, we could be talking generically about "all warning labels on food", in which case we don't need "the"; or we could be talking about "the warning labels that you find on food (not on other products)", in which case we need "the".