Every time I start the game, the player falls just a little down and down in to the ground. Why is that? How can I prevent it?
There are a few possible reasons:
Your character/player does not have a collider on it.
Your ground does not have a collider.
If your ground is a map you made yourself, then you will need to turn on Colliders within the model settings (Click on your model within the project, and in the inspector, apply collisions.
Also, make sure all the colliders are no a trigger (if you click on a collider object, within the inspector, make sure Is Trigger is OFF)
See if that works.