Does Anointed Gear Stack?

That will stack with what is on the weapon even if its 50% incendiary on weapon as well. They count as different anointments because 1 is for "a short time" while the weapon version is for "the next 2 magazines."

Do same Anointments stack?

It appears that, at least in the case of this particular anointment, you CAN NOT stack the effects of the same anointments, but you CAN stack similar anointments. No bonus were applied from holstered weapons.

Do you need to have an anointed weapon equipped?

When activating your action skill you need to have the weapon with this anoint equipped or else it won't trigger. When you swap weapons while your action skill is still active you will lose the bonus even when you return to the weapon with the anoint. With this anoint you get 35% damage reduction.