I think most French people would say: “Il a l’air de quoi?”, or more formally: “De quoi a-t-il l’air?”.

This could however be interpreted as pertaining more to the physical appearance of the person. A way to ask the question that may be closer to your emaning would be the say: “Il a l’air comment?”, although this is not particularly formal.

I would say “Comment a-t-il l’air d’aller ?” or simply “Comment va-t-il ?”.

“De quoi a-t-il l’air ?” is possible too, but it refers more to the physical appearance.

In French, "air" would be the right word to use, but as it refers to so many different aspects of the person (look, mood, fitness, and so on), you would have to be more specific:

Il a l’air heureux ? (Familiar)

A-t-il l’air heureux ? (Formal)

Which would translate to

Does he look happy?

Avoir l’air is a rather ambiguous expression to use for a question. The question might also be about someone’s appearance or intentions, so it’s hard to tell what kind of answer you are seeking.

If you are specifically asking about a person’s mood, you could ask

Quelle est son humeur?

I’d say “Il a l’air comment? Joyeux, triste ?”