So a literal word-for-word translation would be "What's Stephanus doing?", is that right?
Yes, agere is often "do." It's a very generic verb that's used in many different situations.
You get marked wrong if you translate it as "what is stephanus doing?" though.
So the translation could be similar to the English "how do you do, Stephanus?"
No, in your sentence you are talking to Stephanus, in this Latin sentence you are asking someone else about him.
I keep wondering which modern language and strain of accent comes closer to both classical Latin and sermo vulgaris, maybe romanian, catalan or castillan... but the english accent really seems off.
Yeah, the American accent (together with the new "classical" pronunciation) is pretty jarring to me as well.
Czech actually has quite similar word stresses as Latin. And the grammar is quite similar as well. Or, at least it has declination, conjunctions, and so on as well.