I'll try to answer these as best I can, take it fwiw (which isn't much)...
(1) Does the Orthodox Church recognize the leader of The Constantinian Order as an heir to St. Constantine?
(6) Why is The Constantine Order so close in actual distance and in term of friendship to the Pope? Shouldnt they be in Constantinople?
I'm not sure what the Constantinian Order is?
(2) If a new Byzantine State was formed, would it have an emperor, and if yes, would this emperor be the head of The Order?
Regarding the first part, yeah I would assume that there would be an Emperor/Czar should the Byzantine Empire be revived. Then again, I've never given it much thought as I don't expect it to happen.
(3) Does the EP have control over the other Patriarchs, or are they all equal?
In theory they are equal. However, in practice this doesn't always work. It looks pretty petty to have people arguing over who sits where or who signs first, for example. Also, what if there is a dispute and calling a council is inconvenient, or a council has already been called and didn't solve anything? Because of problems like this, while the Ecumencial Patriarch is theoretically equal to all other bishops, in practice he has some powers that other bishops don't. So, they are all equals, but the EP is the first among equals. He has a primacy of honor, rather than a primacy of real power. He wields his primacy through the agreement of all his fellow bishops.
(4) Can an orthodox person be excommunicated?
Yes. Though that would be up to the bishop I would think. It's probably very rare for someone to come right out and officially and authoritatively be excommunicated.
(5) Is Orthodoxy in general a Conservative or Liberal religion?
Conservative. Though traditional might be a more accurate word, as many Orthodox would not identify with the "conservative" political movement in America.
(7) Does Orthodoxy still see the Pope as one of the five Patriarchs?
Generally speaking, no. Sometimes we call him a bishop out of politeness. Sometimes we do so out of ecumenicity. But, there was a schism in which (from an Orthodox perspective) Rome seperated herself from the Church, thus we do not consider her part of the Eastern Orthodox Church, thus she cannot be considered a Patriarch in that Church. However, we await her return to the Church, and the Orthodox hve not since the schism set up another Bishop in Rome (unlike Rome, who didn't mind setting up Latin Patriarchs when the Crusaders sacked Eastern Patriarchates and deposed the rightful bishops).
(8 ) Ive heard you have to feast be be Orthodox. When is this, for how long, and is there a certain food that is forbidden altogether?
I'm not sure which custom exactly this refers to. Asking a priest would be your best bet, as he would be giving the direction that you would have to follow were you to become Orthodox, and the customs at his parish might differ from the next one down the road on such matters.
(9) Are the emperor and the Patriach considered equals?
Well, there's no emperor, so this seems more like a historical question? In theory, no, the Patriarch is supreme in that he guards spiritual needs while the Emperor guards bodily needs (some saint or other said that, St. Photius maybe). In practice, the Emperors usually stuck their noses in the Church's business more than an Orthodox Christian would normally care to think about. Sometimes it worked out well, sometimes it didn't. But in theory, it should have never happened unless the Church asked the state to intervene.
(10) Is there a person higher than the Patriarch on Earth? (Excluding the emperor, if he even is higher)
Higher in what sense? Even a simple lay person can be higher in a certain sense, if they are more faithful and pious. Generally speaking, a Patriarch has a very great honor. Yet, if we read St. Ignatius, some of the amazingly honorific language that St. Ignatius applies to Bishops are also applied to (relatively speaking) lowly deacons.
(11) I was never Catholic, but I was raised and considered by my family to be one. I have always gone to a Catholic Cathedral, and only to an Orthodox one 2 times (Greek). Will I not be considered a "full" Orthodox Christian because of his?
Well, it is important to be "received" into the Orthodox Church if you want to be Orthodox. You can talk to the priest about this, as there are different methods for reception depending on different factors. ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€š Generally you would be made a catechumen first for a period of time, and then later be received in a special service.
(12) Do Orthodox pray the Rosary?
Generally, not really, though that'd be something you could ask a priest about. Orthodox tend to do things like say Canons or Akathists, Pray the Hours, say the Jesus Prayer, etc.
(13) I am going to Istanbul this summer. Do you think I will encounter hostility if I wear a cross in public?
I'm sure someone around here can answer that... . .
Sorry for the many questions, but I want to have some key questions answered before I finalize my decision to become Orthodox.
Don't be sorry!
Asking questions is a good thing. Better to ask them now and know what you are getting into, than to suddenly have questions pop up later and cause confusion and possibly doubts.