If I have a Negator in play which is dealt 3 damage, can I:
Sacrifice the Negator as the first permanent that has to be sacrificed and spare the other 2 sacrifices this way? or should I sacrifice 3 permanents regardless if I sacrifice the Negator or not?
When phyrexian negator is dealt damage, its ability triggers. A triggered ability exists independent from its source on the stack (meaning destruction of the source does not change it).
So if its dealt 3 damage, a trigger goes on the stack to sac 3 permanents. When it resolves, the game tells you to sac 3 permanents, regardless of the condition of the negator.
# 402.6 - Once activated or triggered, an ability exists independently of its source as an ability on the stack. Destruction or removal of the source after that time won't affect the ability. Note that some abilities cause a source to do something (for example, "Prodigal Sorcerer deals 1 damage to target creature or player") rather than the ability doing anything directly. In these cases, any activated or triggered ability that references information about the source will check that information when the ability resolves, or will use the source's last known information if it's no longer in play. [CompRules 2003/07/01]