How does one classify the words in "how about" and "what about"?

I see in other posts that "how", while typically classified as an adverb, can be considered an adjective when paired with a "be" form (e.g. "how is the pizza?"). But in the case of the phrase "how about tomorrow" is "how" an adverb? And what is the appropriate classification of "about"? Finally, does this change if you add to the phrase an ‘s, as in "how’s about tomorrow" (which may not be entirely grammatical, but common in informal speech).