It should be true for all Eastern churches, but here in the United States most churches have pews (which are not used a whole lot - we sit only during the homily, Epistle, and a couple litanies, and some people only sit during the homily - but they can be rather constraining; we should be free to walk around and venerate the various icons during the Liturgy).
There are two kinds of prostrations - minor (bowing low to the waist and touching the floor) and great. A great prostration is the kind of prostration Muslims make that is probably a familiar image to you; they learned it from us.

Usually in America we see people making minor prostrations upon entering the church and before communion, and often at the epiklesis (there are actually supposed to be two or three set times according to the Ruthenian bishops, but nobody knows when they are and uniformity on the part of the congregation is not a part of the Eastern tradition for anyone except the Old Believers). The Old Believers will make a great prostration upon entering the church and then again at the beginning of the Liturgy; we only make great prostrations when venerating the Cross on the second sunday of Great Lent and then again in October on the Triumph of the Life-Giving Cross (same feast as in the Western Church).
After Liturgy many people, especially women, will find an icon on the iconstasis to venerate and pray in a great prostration in front of it (it’s more common for men to stand).
We stand, and if you have the opportunity to come to Liturgy please do so as well; it is our gesture of reverence and would actually be more reverent than kneeling. Kneeling and standing have different meanings in the East than in the West; standing during Communion doesn’t feel as irreverent to me as it does in the Novus Ordo Roman Mass (where I kneel for Communion instead).
I also admire those things in Islam. My understanding is that the Copts do take their shoes off - I think it is a beautiful custom. The Old Believers separate men and women, and it is strongly encouraged everywhere for women to cover their head with a scarf or mantilla. The only non-Catholic Liturgy I have ever been to was at an Armenian Apostolic Church, and someone was standing at the back of the Communion line with a pile of mantillas (chapel veils) she gave to every woman who was not wearing one so that the would present themselves appropriately for Holy Communion. As far as I know only the Armenians made it
mandatory, but it is really best no matter where you are (East or West) for the women to cover their head. In churches of the Roman Rite the mantilla is traditionally worn loose and resting on top of her head; in Eastern churches it is traditionally tied under the chin.
Well, we’re the ones they learned everything from! If the great prostration looks a lot like the Muslim prostration, and if their hand gestures sometimes look similar to the way we fold our arms across our breast while praying, there’s a pretty good historical reason for it!