Aurora 77, once again your unfailing patience and politeness are an example for all on these boards to follow. I'll try to answer some of your questions - addressed to someone else - I'm not as polite as you :).
Please note that these are my opinions and experiences, and while some may agree or follow similar perspectives, there are many who do not, and I have no interest in telling them they are misguided.
"Given what you said about not studying other religions, do any Orthodox Jewish scholars (at universities for instance) study other world religions in the context of writing about or researching world history?"
My answer to this is a bit complex. I will give you two examples of Frum, even chareidi scholars who did study early christianity in the context of their work. Professor Solomon (Zalman) Birnbaum z'l who taught Paleography at the School of Oriental Studies at the University of London many decades ago was one of the foremost scholars of Paleography at the time and he worked on the Dead Sea Scrolls. In this work he encountered and studied texts that were among those sectarian (non rabbinic) writings that some early christians used to formulate their doctrines. He was quite frum, his sons were members of Agudath Israel synagogues, and his grandsons studied at Prominent Yeshivas.
Another orthodox scholar of the Dead Sea Scrolls who has had plenty of exposure to early christian writings is Professor Lawrence Shiffman, longtime scholar at NYU and recently appointed to an administrative position at Yeshiva University. I have and I've read a number of his books, and though his focus is on the early history of Rabbinic Judaism, he has clearly referenced his study and knowledge of early christianity in them, as well as broadcast interviews I have seen. He is also a proponent of centrist rather than modern orthodoxy, putting him in the camp of Rabbi Schacter, among others.
Finally, though I don't know what stream of orthodoxy he considers himself to be in, Professor Noah Feldman is one of the foremost scholars of Islamic legalism in the world. His reputation is quite impressive, and I've heard his analysis owes much to his study of gemara (talmud) and the intricacies of halachic legal codes.
As a historian myself, I've studied Islam and christianity in the context primarily of how they interacted with Judaism and secondarily on how they impacted on Military, Scientific, Economic, Political and Social trends over the last 2000 years.
" It kind of sounds like this kind of thing would not be allowed, but what if the study/writing/research is done with the purpose of better understanding causes and effects in history, especially Jewish history across the millennia?"
One of the things you don't mention is another of the reasons I studied christianity, and that is to learn how to refute missionaries. I have worked with a few anti-missionary organizations. The Rabbis at Jews for Judaism and Outreach Judaism (all of whom are orthodox), for example, have all studied christianity, have clarified Paul's perfidious anti Semitism that infected the church, and have developed ways to combat christian missionaries preying on Jews who have no background or affiliation, passing off their "messianic" Judaism as something other than christianity.
Again, as a historian, One can't fully understand the history of Judaism in the Diaspora without understanding where christian animosity, and later muslim animosity towards Jews came from
"For the non-Jewish people who follow the seven Noachide laws, are they allowed to go further and take up some more of the Jewish obligations, for example keeping the Sabbath?"
I will suggest that you ask this question of your local orthodox Rabbi. For yourself, considering what you have told us about your family history, I would suggest consulting with a Rabbi to determine what your status is.
"Regarding weddings, can an Orthodox Jew attend (I don't mean partake in any of the ritual aspects of, but be present and silent at) an extended family member's or friend's wedding if it occurs in a church?"
There are some (few) sources who might permit being in a church building without participating in any ceremonies or being there while they are going on. Apparently Rabbi Sacks found a halachic rationale for attending a royal wedding, but I am not aware of anyone else who permits it. Though I have been invited to christian weddings, I have never been to one, and I don't expect I would ever go.
"I understand what you said about there being no one deity who satisfies all of the world's people's idea of what a deity is. That being said, when people of different faith backgrounds gather at a vigil, for instance, and a representative of each group speaks in general terms about the love of G-d for people and praying for others' comfort in times of grief and sorrow, does this kind of event jeopardize the separateness of which you spoke?"
For me, no. For others here, likely yes.