Question 1) What was the bullet's flight time? 2) What was the bullet's speed as it left the barrel?

Question

A rifle is aimed horizontally at a target 50m away. The bullet hits the target 2cm below the aim point.

Answer 1

That question is vague at best. Flight time and speed are determined by the velocity of the round fired as well as the length of the barrel. Those variables have to be know in order to answer that question.
Here's the formulas for figuring out velocity and acceleration. Hope it helps.

v2 = vo2 + 2as

where:

v is the muzzle velocity
vo is the initial velocity of the bullet, which is zero
a is the acceleration
s is the barrel length

Since acceleration is the desired value, the derived formula is this:

a=v2/2s

Answer 2

Ignoring all other factors and assuming that the rifle is aimed correctly, etc., the drop below aimpoint tells you the bullt fell 2 cm during its flight. Since the vertical behavior of the bullet is only affected by gravity, you can figure out how long it took to fall the 2 cm.

The time calculated for the fall is the same time it took to travel 50 m, so you can calculate the horizontal velocity of the bullet.