I came across Timothy Jay Alexander's questions about solidifying Hellenismos--as posted in my post about standardizing Hellenismos--last night, and suddenly remembered I had been meaning to answer these sometime soon. I totally forgot about it, so lets do it now. I'm sure I don't need to say this, but everything in this post is personal opinion, and while this applies for my practice, I have no say what so ever over the practice of others, nor do I want to.

At a minimum, how many Greek Gods need to be worshiped for a practice to be Hellenismos, and which ones?
There is a movement in Hellenismos that says the Twelve Olympians--Zeus, Hera, Athena, Hēphaistos, Hestia, Aphrodite, Poseidon, Ares, Demeter, Hermes, Artemis, and Apollon--as well as (perhaps) Dionysos, and Hades, are the only Theoi that need worship within Hellenismos. I am not part of that movement. As far as I'm concerned, Hellenists should give proper appeasement to all Gods, Goddesses, Titans, nature spirits, heroes, kings and queens that were worshipped in ancient Hellas. Many festival days may have been lost to us, but many were not. Follow the sacred days of the month, and the festival schedule and you'll come around to most of them throughout the year. So, at minimum? Fourteen; the ones listed above. At maximum? Every single one of Them.

Does every practitioner of Hellenismos have to honor Hestia? How about Zeus?
Yes, and yes. Why? Because the ancient Hellenes did and Hellenismos is a Recon faith. Hestia was honored in every single home. Children, a new wife, and new serfs were introduced to Her sacred flame within the household. If that flame went out, the kurios of the family went out to the Prytaneion, where Hestia's fire was kept for the city. Zeus, well, Zeus is head of the Twelve Olympians. He's the King of Gods. To me, it's perfectly logical that Zeus receives every honor possible.

Is there a specific ritual style?
Yes. There is a (short) procession to the altar, then there are purification rites, prayers and hymns, sacrifice/offerings, prayers of supplication and thanks. The jury is still out on animal sacrifice, so I'll hold off on including that one.

Can rituals be innovative? If they can, when does innovation cross the line?
This is a hard one. Innovation is a necessity; we can't practice our festivals and sacred days like the ancient Hellenes did. We don't have the community, temples, or days off from work for it. So yes, innovation within Hellenismos is allowed and required. Then again, within ritual, there is a standard format (see above) that should be maintained. It's perfectly possible to do so for any practitioner. The difficulty comes when a practitioner wants to include elements from other Traditions (like circles, but for that specific one, see below) into the ritual. When is the practice Hellenic Polytheism, and when is it Hellenismos? How much Recon needs to be in your practice before it's Hellenismos? I don't know. Personally, I would say that if you do regular concessions to the ancient Hellenic practice for reasons other than necessity, you're practicing Hellenic Polytheism (or, perhaps, Reformed Hellenismos), and if you stay true to the source material unless you absolutely have to, you're practicing Hellenismos.

Can a person cast a circle?
I have a pretty clear opinion about this, which I will nuance for the purpose of this post. My answer is that--if you want to practice Hellenismos--you should leave the circle in the (Neo-)Wiccan Tradition it belongs in. Why create a containing space for the Theoi when calling on Them will not bring forth the dangers associated with summoning the God and Goddess? Why confine Deities which were never confined in the past? Creating a sacred space is fine, but calling corners and dragging watchtowers and/or elements into Hellenistic ritual seems utterly useless to me--and terribly condescending. Your milage may vary.

Are sacrifices and offerings required?
Yes, yes, yes, yes, yes. Can I make this any clearer? Yes! Do the Theoi require it? No, most likely not, but even if it isn't something we do--as a Recon Tradition--because the ancient Hellenes did it, it's a sign of devotion, one of the basics for kharis, and a vital part of daily ritual and Hellenic rituals.

Is there a specific ethical system?
Hellenismos is known for its highly developed ethical system, derived from ancient scripture like the Delphic Maxims I keep going on about as well as scholarly works like the Homeric Hymns, the Tenets of Solon, the Ethics of Aristotle (1,2), the Golden Verses of Pythagoras, the Philosophy of Epicurus, the Stoics, Works and Days by Hesiod and many, many others. Amongst the ethical system, I count living your life in line with the pillars of Hellenismos, one of which is 'Ethike Arete': character excellence. from 'Virtue Ethics: Insights of the Ancient Greeks' by Raymond J. Devetter:

"A character virtue can be thought of as a state (a hexis) created in our psychological lives (our 'souls') over time by performing repeatedly certain actions. There is no official list of character virtues--Aristotle identifies more than a dozen--but three of them play a major role in most all versions of Greek ethics: temperance, courage, and justice."

Are there specific sacred texts?
Besides the ones above, there are a great number of ancient texts that are a staple in every Hellenists household. Hómēros' Odysseia and Iliad come to mind. The works of Hesiod, the tragedies, comedies and surviving satyr plays are another source of information about the ancient Gods. Are these texts sacred in the sense that the bible is sacred? No, there is no holy book within Hellenismos. There is just mythology, preferably from ancient sources.

Can new mythologies be incorporated?
This depends on your definition of new, I guess. Personally, I'm even careful with Roman mythology about the Theoi, so if the question is asked in regards to UPG, then my answer is no. Within the Hellenistic community, UPG is almost completely ignored. It may play a role in individual household worship but does not enter into the religion at large. Only UPG from the ancient Hellenes is used to base the religion on. I think it's valid to say that anything the ancient Hellenes did, was based upon UPG, too. Oracles made predictions, rulers made declarations and myths came into being to explain why certain days were special or how major spheres of influence came to be. 

Is there a specific festival calendar or calendars?
There are several, actually. The Athenian one is the most complete, but there are various surviving calendars. Making a combination of these is most certainly allowed. Integrating a monthly calendar of sacred days is also encouraged. Here at Baring the Aegis, I have supplied an Athenian+ calendar, as well as a calendar of sacred days, for your practicing pleasure. You can find it here.

Can you create new festivals? If you can, what are the limits? Are there limits to what is appropriate? 
Regular readers know that I don't look favorably upon invented, modern, holidays for the Theoi. It's not called a Recon faith for nothing, after all. Still, that's personal opinion and many Hellenists enjoy the various modern day festivals a lot. Another trend seems to be to honor certain deities on secular holidays having to do with their domains. Mother's day comes to mind. I take no issue at all with this if sacrificing to the Theos or Theia in question is a household decision you have made for/with your family. Within your household, you can give sacrifice to whomever you want on any day you want, after all. I'm not a big fan of generalized sweeping statements that proclaim 'mother's day is sacred to [Deity x]', simply because it ascribes a modern invention to the Theoi, who may or many not appreciate being gifted a certain day at all.

So far, my answers to Timothy's questions. How would you answer these from your personal practice?