Little Light was able to sing because Timothy sang his musical number to him
That actually does make this confusing Plot Hole make sense, as Timothy sang to Little Light after he noticed that he glowed. Little Light was originally going to narrate the story instead of Timothy's older self
That might've explained why his voice actor, Eddie Korbich, was miscredited as the voice of the narrator. The "Parade of the Ornaments" scene and Little Light's musical number was one of Timothy's dreams
Prior to those two scenes, Timothy's mother did tell his son to believe while she was tucking him to sleep. This film suffered from Troubled Production
The likely reason why the animation and character designs were bad was because either the budget was spent on the voice actors or it was originally going to have more effort, but the executives forced the producers and animators to rush the film so that it can be released just in time for Christmas. Little Light is named after the children's song "This Little Light of Mine"
This film was shot in Motion Capture
That might explain why the character designs were realistic in this film.