1-read again, knowledge on gates is useless in sakura's case
2-yes it'll break her neck, its deadly injury even for someone like tsunade let alone sakura who absolutely showed no regeneration feats
3-it was a serious injury but a human body would live for seconds before dying if he/she got stabbed but in the breaking neck case death is instant.
Therefore she won't have time to regenerate, and I'm being generous since we absolutely have no proof that sakura is on tsunade's level (sozo seisai)
If she's not dismembered, then there's literally no reason she can't heal it off, and no. I don't know where this came from (probably fiction) but a broken neck is NOT instant death. Plenty of people have survived broken necks in real life. Sasuke slammed Naruto into the ground head first in the anime and he healed it off via Kurama's power. The time you die depends on you, and your injury's severity, but it's never instant.
In fact, damaging the spinal cord is worse, and that's exactly what Tsunade had. She had two blades running through her torso/mid section area, thus her spinal cord was literally severed, yet she was moving and punching.
Sakura reached Tsunade's level of regeneration the moment she unlocked the same jutsu Tsunade uses.
So no. Reverse, Extreme, no Lotus is taking Sakura out.