Quid agis should be fine as well.
Yes, I was also taught Quid agis.
What is the function of "te" in this sentence?
I'm not positive, but I think it's the vocative case.
Literally it says "How do you have yourself, Marcus"?
It is accusative.
You're right, mea culpa.
It should be a kind of reflexive, not directly accusative, I suppose.
Think that the verb is not just "habere" but reflexive "se habere" which has a meaning like "to feel (self)". Just like French "Tu te sens bien." (You feel good). Similar structure (but just different word).
in the notes says you should use QUIS AGIS for what are you doing, not for this sentence.
and, why Marce? there's no one else, it should be Marcus