Etymology
The English word of Easter is believed to be derived from the name of the Pagan Goddess Ēostre She is believed to have been a germanic deity who presided over either spring and fertility or the sunrise. On the germanic calendar Ēosturmōnaþ the rough equivalent of the month of april was named in her honor. It is interesting to note that while it is widely accepted that the name of Easter comes from this goddess some scholars believe that she was actually invented after most people in the regions she would be worshiped in were converted to christianity. It is also worth noting that outside of English few languages use Easter(or similar terms) to refer to the holiday and instead use words derived from the Greek and Latin Pascha meaning Passover.
Easter Eggs
Comparatively Easter eggs have a simple history the practice began as early as the 4th century. In the beginning the eggs would only be died red to represent the blood that christ shed and his resurrection. This practice became officially part of the holiday in 1610 as the work of Pope Paul the fifth. Since then the coloring and use of Easter Eggs has expanded to the variety that we find in our modern culture.
The Easter Bunny
The Easter Bunny originated in Germany with him taking a role very similar to that we find in Santa Claus today. He would judge if children were good or bad and if they were good leave them presents and colored eggs in the night for them to discover come morning. The first mention of the tradition comes from a book written in 1682. The choice of a hare as the symbol of Easter is believed to stem from the false belief in ancient times that hares were hermaphrodites and as such could reproduce without losing their virginity which created an association between them and the Virgin Mary. They were also seen as symbols of fertility showing the better fertility of soil that came with spring. The idea seems to have spread quickly as there are records of it having reached America as early as the 1700's.