moons orbit planets and planets orbit the
sun. is kepler’s constant the same for both
circumstances?

What Kepler's constant ? ? ! ?

The only constant in Kepler's laws is in the third one, where it says something to the
effect that (square of a body's period) / (cube of its distance from the central body)
is a constant.

That means it's a constant for multiple little ones orbiting the same central body.
But it's not the same constant for other central bodies.

It's one constant for the planets, asteroids, and comets orbiting the sun.

It's a different constant for the moon, TV satellites, weather satellites,
and military satellites orbiting the Earth.

Since you have not included the experiment situation and the data, of course, i can not give you specific details about it. but i can you with this question.1) i will assume that the motion is projectile (parabolic) motion.2) yes, the horizontal distance depends on the horizontal velocity as, naming vx the horizontal velocity and t the time, it is: x = vx × t3) now, observe that the flight time depends on the vertical velocity as, naming voy the initial vertical velocity, t the time and y the vertical distance before reaching the ground: y = yo + voy×t - gt² / 2.the higher the initial vertical velocity (voy) the longer the object will be flying and so t will be higher in the equation for the horizontal distance.that explains the relationship between the horizontal distance and the horizontal velocity.

Ineed more information about  the question