Keep in mind:
Max Health = Health + Shield
Health can be from 1 - 100
Shield can be from 0 - 100
Mini Shield gives you +25 Shield until you are at 50 Shield.
Big Shield gives you +50 up to 100 Shield
AR (assault rifle) deals 33 damage
A Purple Shotgun deals 30 - 200 damage (in this scenario 110 damage)
A Gold Rocket deals 130 damage
A Cracked shield means you have 0 Shield remaining

USE SLOW MOTION TO WATCH

When Fresh’s opponent drinks a mini shield - (pause at 5:48/49)
What are the maximum and minimum his health could be?

26 - 150 HP
Your max health is 200. A Mini Shield gives 25 Shield, but only up to 50
Shield, meaning no matter what Shield level a player starts at, the player
can only gain up to 50 Shield by popping a Mini Shield. So the least possible
Max Health the player can have in this situation is 26 Max Health
(1 Health + 0 Shield + 25 Shield from the mini = 26 Max Health), and the most
possible Max Health the player can have is 150 (100 Health + 25-49 Shield +
25 shield from the mini = 150 Max Health).

When Fresh shoots his opponent - (pause at 5:49)
What are the maximum and minimum their health could be?

1 - 40 HP
You take the answers from the previous question and subtract the amount of
damage the pump shotgun does. In this scenario, the pump shotgun does 110 damage.
Because they are still alive, we know they had more than 110 health, so the new
possible minimum Max Health they have is 1. (This would mean they had at least 111
health previously). The Max Health they could now have is 40 (150 - 110 = 40).

How many more AR shots will it take to eliminate them?

1 - 2
If an AR (assault rifle) does 33 damage at minimum, and they are between 1
and 40 health, they can possibly be downed with one shot, and a guaranteed
down with 2 shots. This is because 40 - 33 = 7, so they might survive the first
shot if they have Max Health 40. But if you hit them a second time, they will
certainly die because 7 - 33 < 0.