Not more than a modern people in England have difficulties understanding Shakespear.
Knowledge about religious rituals is granted only to the priesthood.
Not true at all. You must be either twisting the facts or be completely misinformed. There are so many ways -- starting from going to lectures, organised by Church, down to reading websites and finally - going to the church and simply asking the priest.
Bibles in modern Russian are available only in protestant churches as well as the theological explanation of the Christianity.
Not true at all. You can literally go to any bookstore and in there you will be offered a selection of holy books for different religions. As well as ordering these books online.
As well as going to the nearest Orthodox church (and not not only Orthodox) and buying it at the store which nearly every one of them has. Typically these shops would be selling candles, reliogious books, crosses (and other symbols) as well as taking orders for prayers and masses.