I'm Episcopalian, and we do indeed have a Christmas midnight mass. The mass involves the use of specific liturgy and follows a certain format that includes Communion as the core of the service. Since you seem to have some confusion about various denominations and how they relate, I'll try to give you a brief overview of the Episcopal, Anglican, and Catholic Churches' histories.
The Catholic Church is the mother of all Christian churches. Although many Protestant churches are vastly different in style and function, they come from the original foundation of the Catholic Church that was first institutionalized under the leadership of the Roman Empire. The Anglican Church (also known as the Church of England) was formed by Henry VIII in England in 1534 when the Catholic Church refused to grant him a divorce from his first wife so he could marry his second wife. Henry also wanted the money from the monasteries, but that's another story. The Episcopal Church is an American creation that traces its roots to the Revolutionary War. Originally established as the Church of England in the American colonies, it became officially the Episcopal Church after the conclusion of the Revolutionary War. The Archbishop of Canterbury refused to ordain an American bishop, so the Americans turned to Scotland for the ordination of the first Presiding Bishop of the Episcopal Church.
The head of the Catholic Church is the Pope. The head of the Anglican Church or Church of England is the Archbishop of Canterbury. The head of the Episcopal Church is the Presiding Bishop. All three churches share certain common beliefs and practices:
They all believe in one baptism for the forgiveness of sins. In general, baptism is performed on infants or young children.
They all use a liturgical service. In a liturgical service, prayers and excerpts from the Bible are read aloud by the priest and/or congregation throughout the service. The order of these readings is nearly always the same, coming in the same sequence. The Episcopal Church uses the Book of Common Prayer for its liturgy. You will find all of the prayers, psalms, orders of service, and statements of belief in there.
All three churches believe in the Trinity: the Father, the Son, and the Holy Ghost. The Father is God. The Son refers to Jesus Christ, and the Holy Ghost refers to a a spiritual advocate that aids in our communication with God and Jesus.
All three churches believe in apostolic succession. They believe that the leaders, bishops, and priests are ordained in a logical succession inspired directly from the original apostles in the New Testament.
All three churches hold communion as the core of their services. Communion consists of a prayerful partaking of the body and bread, which represents the body and blood of Jesus Christ as his sacrifice to forgive us for our sins.
Please note that I'm not a theologian. These are my interpretations of beliefs, but I think they're pretty close, based upon my teaching.
Now, let's walk through an Episcopalian midnight Christmas Eve Mass. In my church, we celebrate a high mass, which means we have incense and parts of the liturgy are song, not spoken. I'll take you step-by-step through a midnight mass at my church. Ready?
The service usually begins at 11:00 p.m. on Christmas Eve, and yes, people dress up. In the Southwest, where I live, the exterior of the church is adorned with luminarias, but other churches may just have standard creches and Christmas lights outside.
Music is playing softly when we enter the church. An usher may escort us to a pew, or we may find seating on our own. We are handed a program for the service before we go in. Inside the church, we kneel briefly for a silent prayer known only to us and God.
The organ brings up the music--a cue to rise--and the formal procession begins. The procession includes acolytes (people who help with lighting of the candles and other parts of the service), deacons, priests, and the choir. As the procession enters from the rear of the church, the congregation and choir sing a hymn from the hymnal that is stored in a slot on the backside of the pew in front of us. A favorite hymn for Christmas Eve mass is "O Come, O Come, Emanuel"--all 11? verses! In high mass, the procession is led by the censor who fans incense out on all sides of the aisle. The incense represents the spiritual essence of God.
After the hymn, the priest stands at the podium in front and says the Collect for Purity. We then sing the Gloria, a hymn of praise I believe is also used in the Catholic mass. The priest then says a special prayer for the day (in this case, a prayer relative to the Christmas service) and directs the congregation to be seated.
Next is a reading from the Old Testament. During Christmas Eve mass, this reading is usually from Isaiah 9:2-7, the portion that talks about the Prince of Peace.
After the Old Testament Reading, there is a reading from one of the Psalms. In high mass at my church, the Psalm is sung by a member of the choir. In a more traditional service, the Psalm may be read aloud by the congregation. Sometimes the Psalm is read or sung responsively: One person sings or speaks one verse, and the congregation responds by singing or speaking aloud the verse that follows.
Next is a reading from the New Testament, usually from Hebrews. Again, the reading is relevant to the birth of Christ. At the end of the reading, we say, "Praise be to God."
Everyone then stands and we sing a few verses from another Christmas carol before the reading from the Gospel. The reading of the Old Testament and the Psalms (if they're read aloud) take place at a lectern at the front of the church. For the reading of the Gospel, the priest walks down the aisle toward the center of the church during the singing of the hymn or carol. After we sing 1-3 verses, he reads from the Book of Luke in the New Testament. At the end of the Gospel reading, we say, "Praise be to Christ."
The sermon is next, presented by the priest at the front of the church. For Christmas Eve mass, it tends be short and a reflection about the birth of Christ. We sit during the sermon.
Once the sermon is concluded, we stand and recite the Nicene Creed, which is a statement of our beliefs. I think the Catholic church uses the same statement. Then we kneel again while prayers are offered by a lay reader and/or members of the congregation for the world, the departed, and for those who are close to us. When these are concluded, the priest may direct to congregation to stand or kneel while read aloud the general Confession. After the confession, we exchange the Peace. The priest says, "Peace be with you." We respond by offering him peace and turning to our neighbors to greet them and exchange offerings of peace.
We sit and the choir sings or another group performs while the collection is taken. A collection plate is passed among the pews and members can choose to place a donation in the plate. We stand again when the offering is brought to the altar. Sometimes a hymn is sung during the presentation of the offering.
Still standing, we begin the service of Communion, which starts with a prayer called The Great Thanksgiving. Then we sing the Sanctus (also used in the Catholic Church). We then stand or kneel while the priest recites the story of Jesus of how God sent Jesus for our redemption. This recalls the New Testament story of Jesus sharing the bread and wine, saying, "Take, eat, this is my body, which is given for you." and "Take, drink, this is my blood, which is shed for you and your sins." Afterward, we sing or say the Lord's prayer together. We remain kneeling or standing while the priest calls up to the altar to partake of the bread and wine (Communion). Members of the congregation are led to the altar to kneel and take a Communion wafer and drink the wine (real wine) from a single shared cup. The choir or another musical group performs while this is taking place. Once we receive Communion, we return to our seats.
When everyone has received Communion, we read aloud the Prayer of Thanksgiving. During Christmas Eve mass, the lights in the church are lowered then and the congregation sings "Silent Night." Some people kneel. I've also been in churches where candles are passed and lit during the singing of "Silent Night." It's now close to midnight.
There is a moment of silence after the singing. The lights are brought up and the priest dismisses us. We sing a final carol, often "Hark the Herald Angels Sing" or "Joy to the World," and the recession of priests, acolytes, choir, etc. leave the church with the congregation following them. That's the end of the service.
Although my church doesn't do this, I used to belong to an Episcopal Church that hosted a feast after midnight Mass, which was a lot of fun. The children brought sleeping bags to the parish hall and held their own short service during the mass and then went to sleep. We then woke everyone up at the end of the adult mass and stuffed our faces before going home to bed.
Hope that answers your questions. Sorry it was so long!