Its not a heal = Battle fatigue does nothing.
PVP power does affect the damage the strike does but does NOT increase the Healing absortion (Only scales with AP).
Kind of. Oggy is correct that the healing absorb is only based on AP, but the debuff applied indirectly scales with battle fatigue. If you put a 200k stack on someone without battle fatigue, they have to heal through 200k. With battle fatigue that is effectively increased by 60%. This is also why necrotic starts to get stronger and stronger as dampening kicks in. The absorb remains unchanged, but it gets harder and harder to heal through it.
Necrotic Strike debuff isn not affected by Battle Farigue but its is affected by PvP resilience ( one of Hotfixes from 3.0-3.1 dont remember in witch patch it was)