What is it that you want to know about us and our Church? I ask for clarification because I can quote St. Cyril at you until I'm blue in the keyboard, but that's not going to help you understand us if you already believe that his theology is best reflected in Chalcedonianism. Ditto also our liturgical prayers and so on.
(That said, here are some anyway...ha! No, but seriously...maybe their words will help spur a more focused discussion.)
The Syrian Fraction (in English, prayed by Fr. Moses Samaan), from the Coptic Orthodox Church (my church; we call it the Syrian fraction because it originally came from the Syrian/c Orthodox):
The Coptic Sunday Theotokia, Pt. 1 (in English, prayed by the monks of St. Anthony monastery in the California desert; tons of theological statements in here to reflect upon):
Perhaps others from the other churches (Syriac Orthodox, Orthodox Tewahedo...I don't know if we have any Armenians here with us now) can offer prayers from their own church traditions which can help to illuminate what we believe in the ways that they do. For now, I hope this will do to focus the discussion a little bit. Let me know what you think after you have heard and thought of these. To me they are clear, but then I'm already here...
Unfortunately, I don't know of any entry level book for us akin to what the EO have with Ware's
The Orthodox Church or similar. We have very diverse histories and practices and never underwent a distinct period of uniformity as the Chalcedonians in Byzantine Empire did, so we're still just kind of...you know...doing stuff how we do it, e.g., different canons collected at different times, different languages and chant forms (you can't fit Coptic chant into the 8-tone system, for instance), different liturgies, different fasting practices, etc. You couldn't really put that all into one book, or at least not one that would be in depth enough for anyone outside of the communion to understand while not also being very unwieldy. Think of it this way: As the EO often say about the RCC, what we are looking at is centuries of development after parting ways. But whereas the Chalcedonians parted ways with one another into Eastern and Western camps after ~1000 years of being in communion, we parted ways with both of you after only ~500. So we developed differently and more along the lines of what existed prior to the uniformity that later came to your own churches, at which point in time we were of course already out of the picture.