My response if focused from the Catholic perspective.
Are there any church calendars that include Advent as Christmas, or is Christmas always supposed to follow December 25th?
The Day
From the Catholic Church, Christmas Day ("The Solemnity of the Nativity of the Lord") starts on Christmas Eve, December 24th as sundown.
The Season
According to the Catholic Encyclopedia:
In different Churches, the Christmas Season might end on Jan. 6 (the traditional date of the Feast of the Epiphany), or might last until the Feast of the Baptism of the Lord (usually the Sunday after Epiphany), or might even last all the way to Feb. 2 (the Feast of the Presentation of the Lord, 40 days after Dec. 25).
I think it it interesting that the song, "Twelve Days of Christmas" is referring to the twelve days from Christmas to Epiphany.
Historically, did the church celebrate Christmas before or after December 25th?
The Day
From the Catholic Encyclopedia (section titled "Early Celebration"):
The first evidence of the feast is from Egypt. About A.D. 200, Clement of Alexandria (Stromata I.21) says that certain Egyptian theologians "over curiously" assign, not the year alone, but the day of Christ's birth, placing it on 25 Pachon (20 May) in the twenty-eighth year of Augustus.
It goes on from there to list many different dates that Christmas (the day as the Birth of Christ) was celebrated on.
The Season
Codex Theod., II, 8, 27 (cf. XV, 5,5) forbids, in 425, circus games on 25 December; though not till Codex Just., III, 12, 6 (529) is cessation of work imposed. The Second Council of Tours (can. xi, xvii) proclaims, in 566 or 567, the sanctity of the "twelve days" from Christmas to Epiphany, and the duty of Advent fast; that of Agde (506), in canons 63-64, orders a universal communion, and that of Braga (563) forbids fasting on Christmas Day. Popular merry-making, however, so increased that the "Laws of King Cnut", fabricated c. 1110, order a fast from Christmas to Epiphany.
Why has the emphasis on Christmas switched to Advent (the time of preparation)?
I think it is important to note that Advent is not just the time of preparation for Christmas but for the second coming.
According to the USCCB:
Beginning the Church's liturgical year, Advent (from, "ad-venire" in Latin or "to come to") is the season encompassing the four Sundays (and weekdays) leading up to the celebration of Christmas.
The Advent season is a time of preparation that directs our hearts and minds to Christ’s second coming at the end of time and also to the anniversary of the Lord’s birth on Christmas. The final days of Advent, from December 17 to December 24, focus particularly on our preparation for the celebrations of the Nativity of our Lord (Christmas).
[emphasis added]
"Advent, this powerful liturgical season that we are beginning, invites us to pause in silence to understand a presence. It is an invitation to understand that the individual events of the day are hints that God is giving us, signs of the attention he has for each one of us."
---Pope Benedict VXI, Homily at First Vespers of Advent, November 28, 2009
In the weeks before or during the Christmas season, many people set up a "manger scene" which has its origins from the nativity scene erected by St. Francis of Assisi. This could be taken as either a celebration of Christmas or an Advent celebration (many people will put the figures in the manger only at the appropriate times -Jesus on the 25th of Dec, the magi on Jan 6/7th).
