I believe it was Carl Faberge, of the House of Faberge, who made these "Faberge eggs" as they are usually called. See the Related Link below for the Wikipedia entry on the Faberge eggs.
The Faberge eggs were made as Easter gifts from the Tzar to his wife. The Russian royal family was Russian Orthodox religion. They were made by the jeweler Faberge out of diamonds, gems, pearls, and enameled. They had little special things inside of them.
No, Tsar Alexander III was the Emperor of Russia who commissioned the eggs to be made by the House of Fabergé.
Yes. For more info about the Faberge Eggs, see the Related Link below.
The man named Peter Carl Faberge - go Google :)
Faberge eggs are essentially 'dioramas' -- three-dimensional miniatures made from metal and set with precious stones. Faberge was the court jeweler to the Czar of the Russian Empire. Extensive planning and drawing precedes any fabrication, then the process of fashioning the metal, applying any enamel and setting jewels into the 'structure' ensues. You can read more, below.