For the player model, you should freeze camera in 1 spot above the scene and see if player moves the way you want.

And for the camera, there is many ways but i'd start by totally separating it from player. There is ways to make camera stick to the player like a "sphere on a spring". You can calculate the supposed camera position behind the player and then move camera towards it.

This calculation as vectors:
TC = Target Camera , C = Camera
Variable S = Speed (closer to 0 slower, 1 has no delay)

C = C+(TC-C)*S
And same formula for camera angle

Also note that you can change TC on fly! It very smoothly transports camera to anywhere in the world.