"Quid agis?" is a common idiomatic expression meaning "how are you doing" and "what are you doing". It is similar to the French "ça va?" Some of the ways I have heard you can respond are bene, male, bene mē habeō, male mē habeō.
How does one ask how the other person is doing. For instance, in French, one can say:
Ça va?
Ça va bien. Et toi?
Ça va bien aussi.
But how would one do this in Latin? Would one say et tu?, or would one say something else?
To get a good classical answer, a good starting point is the playwright Plautus who has lots of fast-paced dialogue compared to most other ancient authors. This corpus search gives you all the hits for quid agis in Plautus, returning 40 matches (with some false positives).
Here are some examples:
Asinaria 297:
– Quid agis, custos carceris?
– O catenarum colone.Casina 577:
– Quid agis, mea festivitas?
– Te ecastor praestolabar.Casina 801:
– Quid agis, mea salus?
– Esurio hercle, atque adeo hau salubriter.Menaechmi 138:
– Quid agis?
– Teneo dextera genium meum.Poenulus 862:
– Quid agis?
– Facio quod manufesti moechi haú ferme solent.Truculentus 577:
– Noster Cyame, quid agis? ut vales?
– Valeo, et venio ad minus valentem, et melius qui valeat fero.
My conclusion is that there is absolutely no set phrase. A lot of times the question is simply ignored, and it is also common to just state what you are doing. That is, at least in Plautus quid agis? is far closer to a genuine question than a mere greeting than the French 'ça va?'. It is worth noting that, at least after a quick glance, it appears that the question is never returned to the asker. Perhaps there are instances somewhere of an "and how about you?", but it is certainly not common.
As there is no standard, respond in any way you like. You can say that you are doing well, or that you are annoyed with your friend being late, or that you want to do something. Or just move on to what you want to say. A simple way to say "I'm fine" is valeo.
Whatever you do, I recommend being socially aware. If you are greeted by a friend who expects social customs akin to those when speaking English or French, then it is probably best to reply briefly and return the question: Valeo. Valesne et tu? But if you want to follow the standards of classical Latin, do something else.
The suggestions you list are possible, but be aware that they appear to be essentially translations of polite modern responses in other languages. In classical Latin you can get to the point directly and tell more precisely how you feel or what you want.
A helpful resource on this point is Paolo Poccetti, "Greeting and farewell expressions as evidence for colloquial language: between literary and epigraphical texts" in Colloquial and Literary Latin. All my examples are drawn from this chapter.
It's worth noting that elliptical reciprocal greetings seem to be confined to the salutation:
We do find reciprocal asking about health and well-being, but not with elliptical formulas. Usually, the question is answered, then reworded. In one passage, quid agis? is clearly a reciprocal version of ut vales?
TR. di te ament plurimum, Simo.
SI. salvos sis, Tranio. TR. ut vales? SI. non male.
quid agis? (Pl. Most. 717–19)
There is one instance in which we do see an exact repetition of wording, but the context makes clear that it's an unusual play on words:
idem tribuno plebi potentissimo homini M. Druso, sed multa in re publica molienti, cum ille eum salutasset ut fit dixisset: 'quid agis, Grani?' respondit 'immo vero tu, Druse, quid agis?" (Cic. Planc. 33)
When the tribune M. Drusus, a very powerful man but much engaged in political intrigue, greeted him and said, 'How are you doing, Granius?' he responded, 'What about you, Drusus, what are you up to?'
So, based on the admittedly fragmentary evidence available to us from antiquity, it seems that an elliptical reply would not be used to answer "quid agis?".
