Is there any evidence, stated by Blizzard or others, that the cooldown of Spirit Vessel is reduced whenever Grave Injustice is triggered?
No, Spirit Vessel is not affected by the cooldown reduction of Grave Injustice.
Which is a little counter intuitive, as the text on Grave Injustice would indicate that all abilities have their cooldowns reduced:
Fundamentally though, the cheat-death effect of Spirit Vessel is more of a proc than a cooldown. This is backed up in the many build discussions around the use of these abilities together, including this quote:
While Grave Injustice does not reduce the cooldown for the cheat-death proc, it will stack with the cooldown reduction for abilities such as Spirit Walk.
No, Spirit Vessel can not activate more than stated by the tooltip, this is because the ability itself never goes on cooldown, but rather, the witchdoctor gets a debuff that cancels a second activation of Spirit Vessel.