First of all, let's define terms:
Accuracy is a measure of a gun/ammo combination that can hit a designated point, like a bulls eye on a target.
Precision is a measure of a gun/ammo combination that can hit the same spot time after time.
Airgun reviewers shoot for groups to demonstrate precision. They don't care where the pellet lands, only that each pellet lands precisely upon the previous ones. Stacking one on top of the other. THEN they adjust their sights for accuracy; move that tight little group onto a bulls eye.
Regulators assure precision. Regulators assure consistent velocities shot after shot. All other factors being equal, this consistency results in the greatest precision pellet upon pellet, shot after shot.
To answer your second question depends on the weight of your projectile and the distance you are shooting it. You'll learn all about that through experience. For close in work, you can tolerate a lot more ES before the POI changes. For distance, ES becomes very important for all pellet weights.
Remember, all projectiles begin to succumb to the forces of gravity the moment they leave the barrel. They fall at the acceleration rate of 33 feet per second per second. That rate of vertical acceleration is constant until it reaches terminal vertical velocity (maximum free fall speed). For a human jumping out of an airplane without a parachute, the terminal velocity as about 120 mph. When he leaves the airplane, his vertical velocity is zero and quickly accelerates at the rate of 33 feet per second per second until he reaches terminal velocity of 120 mph. From that point he continues to fall at 120 mph for thousands of feet until he opens his shoot of hits the ground. The apparent (not actual) drop of a projectile seems less at muzzle velocities. But as velocity slows with distance, the apparent drop seems higher. Horizontal velocity gradually gives way to vertical velocity. The more consistent the forward velocity, the more consistent the apparent drop at a given distance. Regulators maintain the most consistent velocity shot to shot. And since the vertical rate of drop is consistent and fixed, the point of impact is likewise consistent with a regulator.
In summation: maintain precise velocity, you hit the same hole time after time, all other factors being equal. Regulators are designed to maintain precise velocity; whatever velocity that you set it for.
BeemanR7