Christians started remembering Jesus’ Resurrection every Sunday after it happened. A special day was identified by the Council of of Nicaea for celebrating the special day by 325 AD. However the decision changed into concern for Christians as whether to celebrate the Resurrection on a weekday or on a Sunday.
As Jewish leaders decided on the date of the Passover, the Christian community decided the date for Easter by calculating three days after Passover. This meant Easter would be observed on a different day each year, and could fall on any day of the week.
But many believed that Jesus rose on Sunday and that day had been set as the Lord’s Day, hence becoming the only day to celebrate Easter. Perhaps, some didn't want to celebrate Christian occasion based on Jewish calendar.
So, finally it was finalised that Easter should be observed on the Sunday, after the first full moon. This method is still followed today and hence it fall on different date every year.
Rabbits are associated with Easter. Since rabbit is an ancient symbol of moon and Easter’s date depend on it, it might have helped the hare to be put in the Easter celebrations. For ardent believers, the rabbit coming out of the tunnel symbolise the emergence of Jesus from the tomb.
Egg became a symbol of Easter because ancient culture visualised egg as a symbol of life. Christians believe egg is a symbol with life and hence became a part of celebrating Jesus’ resurrection.