(For those who give up, see answers below.)

 1. ABCDEFGHIJKMNOPQRSTUVWXYZ

 2. On my list, I only desire my foremost dual incisors.

 3. The smogless witching hour has arrived.

 4. Exuberating to this orb

 5. 288 Yuletide hours

 6. Sir Lancelot with laryngitis

 7. Leave and do an elevated broadcast.

 8. That small hamlet south of the Holy City

 9. Listen, the winged heavenly messengers are proclaiming tunefully.

10. Mom's mother was the victim of a "hit-and-run" by Santa's sleigh team.

11. I spied my maternal parent face-against-face with Father Christmas.

12. Whose offspring?

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ANSWERS:

 1. The First Noel   (no 'L')

 2. All I Want for Christmas is My Two Front Teeth

 3. It Came upon a Midnight Clear

 4. Joy to the World

 5. The Twelve Days of Christmas

 6. Silent Night

 7. Go Tell It on the Mountain

 8. O Little Town of Bethlehem

 9. Hark the Herald Angels Sing

10. Grandma Got Run-over by a Reindeer

11. I Saw Mama Kissin' Santa Claus

12. What Child Is This?