Before I continue, I would like to clarify that Greek Tragedies (the music) by and large weren't actually written in Greek, but rather, used Greek stories and legends as plot devices. The revitalization of Greek philosophers and artists in the early Renaissance spurred the creation of madrigal comedies and madrigal cycles in which several madrigals would be strung together with narrated text to make a complete story.
Out of this performance practice emerged two schools of thought by Renaissance scholars. One view was that only the choruses were sung with the rest narrated. This view was put into practice in a 1585 performance in Vincenza of Sophocles' Oedipus Rex with Italian translation. The opposing view was championed by Girolamo Mei (1519 - 1594), a Florentine scholar who edited several Greek dramas. He purported that Greek music consisted of a single melody, either sung by the chorus or the soloist, with our without accompaniment.
Now, approaching your question directly, it is difficult to answer in that it is essentially asking for the formula of interaction between a soloist and an ensemble. The point of the music (a part from showing off the instrument / singer) is the very interaction itself between the soloist and the ensemble. It is going to be different for every piece of music because every piece of music itself is different. If I could say to you, "Yes, every four measures". Music would get pretty boring pretty quickly.
Now, if you're looking for large-scale form that unifies the interaction between the two as a whole, then I would suggest reading into Sonata-Allegro Form as it is one of the most common forms of music from Classical to Contemporary.
Regarding the other parts of your question. It is difficult to answer because you are the only one really who can determine how many scores you need to study. I would study as many as possible for the clearest picture. Girolamo Mei certainly did (and proceeded accordingly, being supported by the Florentine Camerata, notably Vincenzo Galilei). If I had to pick a number, I would say 5 would be a good place to start. As for preserving the integrity of the rhythms, again, you're assuming the music was set to Greek text, which it wasn't. The Greek would have been translated (very likely into Italian) before being put to music. Very few, if anyone actually performed the music in Greek. That said, if you absolutely had to know about the fidelity of the rhythms in Italian to Greek, you'd well, have to be fluent in Greek. That said, even if you were fluent in Greek, you would need to have the exact translation into Greek of the original author. Really overall quite unnecessary.
To aid you on your quest, here are some early examples of opera using Greek tragedy that you can seek out and analyze:
- Jacobo Peri - Dafne
- Jacobo Peri - L'Euridice
- Monteverdi - Orfeo
- Monteverdi - L'Arianna
- Marco da Gagliano - Dafne
Hope that helps.