One can read about their marriage and life in numerous books, including John van der Kiste's biography of Prince Alfred, Duke of Edinburgh. The book, Dearest Affie: Alfred, Duke of Edinburgh, was published in 1984. The late Bee Jordaan was the book's co-author. Queen Marie of Romania's memoirs are also a wealth on information about her parents, and her family. John Wimbles has written extensively on the Grand Duchess and her family for Royalty Digest.
The best article on the marriage itself - from the negotiations to the actual ceremony - you might want to read "A Curious Royal Romance: The Queen's Son and the Tsar's Daughter." This article, which was written by Merritt Abrash and published in the July 1969 issue of Slavonic and East European Review. It is available through JSTOR, to which many academic libraries subscribe.
Make that two ceremonies: Marie and Affie were married twice, first, according to the rites of the Russian Orthodox church, which was followed by a Church of England marriage ceremony.
In terms of religion, the family was relatively ecumenical. Affie and Marie's children were baptised according to the rites of the Anglican church. The couple's only son, young Affie, was sent to live in Coburg when he was a child, and raised there by a tutor (with limited contact with the outside world). Eventually, Affie and Marie moved to Coburg with their daughters, all of whom were confirmed in the Lutheran church. Most of the branches, including the main branch, was Lutheran, so it made perfect sense for Affie's children to be confirmed in the Lutheran church. Queen Victoria did not mind. All of her German grandchildren were Lutheran. Prince Albert was baptised and confirmed in the Lutheran church. Ditto Queen Alexandra. There is no record of Alexandra ever officially joining the Anglican church although she worshipped regularly in the Anglican church. (The differences between the two churches are minimal.)
Queen Marie remained a member of the Church of England. Her marriage took place in a Roman Catholic church because her husband, Ferdinand, was Roman Catholic. As heir to the Romanian throne, he was not required to convert, although he had agreed to raise his children as members of the Romanian Orthodox church. On Sundays, Marie would go to the local Anglican church, while her husband attended Roman Catholic services, and their children would head to the Orthodox church. (Ferdinand's position was similar to another Balkan monarch, King Ferdinand of Bulgaria, who remained Roman Catholic, although he had his elder son, Boris, rebaptised into the Orthodox faith. In fact, both Ferdinands were denied Holy Communion for many years because of their decisions to raise their children Orthodox. All of the Romanian children were Orthodox. Only Boris of Bulgaria was raised in the faith. His brother and two sisters were raised Roman Catholic.)
The second daughter, Victoria Melita, was married twice. Her first husband, the Duke of Hesse and by Rhine (who was her first cousin) was Lutheran. They were married in a Lutheran church, and their daughter was baptised Lutheran. Ducky's second husband, Grand Duke Kirill (another first cousin) was Russian Orthodox. They were married in a Russian Orthodox ceremony, but Ducky did not convert until several months before the birth of their first daughter, Marie.
Alexandra married a Lutheran, the Prince of Hohenlohe-Langenburg, and remained a member of the Lutheran church after her confirmation and marriage.
Beatrice - Baby Bee - was married to Infante Alfonso de Orleans-Borbon, in two wedding ceremonies: Roman Catholic and Lutheran. She agreed to raise her children as Roman Catholic, but she remained Protestant until the 1920s, when she converted to the Roman Catholic faith.