Silent Night, Deadly Night/WMG

Ricky is a Terminator

 * Albeit a malfunctioning one.

Ricky from Part 2 is not Billy's brother.

 * Think about it for a second. Ricky is able to recall events that he really shouldn't be able to, such as the murder of his parents as a baby and various events from Billy's life. He has an undiagnosed mental disorder for many years, which he is mostly able to keep in check (barring the murders he commits early on). It's only when he sees the original Silent Night Deadly Night during the cinema scene that he starts to truly lose his sanity and adopts the backstory from the film as his own.