Question about the 1000 achievement requirement for points.

If i wanted to delete the character on my account with 1000 achievement points. Would i not be able to gain points every day anymore? Reason being because i want to delete my delete my horde death knight to make an alliance one. But that character is my only character with 1000 achievement points.

Which realm are you talking about? You can faction change for 30 points/coins which also include race change and you keep your arch/gear, etc.

if a player has 1 horde DK then he can not make an alliance DK?