Every operator starts with 120 hp however you have 100 hp between you and the down but not out stage.

In the first scenario, excluding all damage reduction due to armor, you get hit by 2 bullets that do 55 damage each(55x2=110=between 100 and 120) . You will be put into the down state with 10 hp(a behind the scenes/invisible number) between you and death. once revived, you have 50 health remaining(75 with doc), total, with no remaining buffer. For this reason an operator cannot be downed more than once excluding being hit by a welcome mat.

In the second scenario you get hit by 3 bullets that do 45 damage each(45x3=135>120), the third bullet will kill you without downing you because you took damage totaling more than the total hp you have.

Armor decreases the amount of damage you take from a single bullet. This is inclusive of the rook armor. Because each bullet does less damage, you have a higher chance of landing within the 20hp "down zone"