Player movement on tilting platform

Hi,

I'm trying to make a player move on a platform that is tilting on the x and z axis and would like the player to:

(1) always be parallel to the ground

(2) don't float/fly when the platform starts tilting

(3) face the direction I'm moving

I don't know if this is the correct way to do this, but for now I'm hoping to achieve (1) by making the transform.up the normal of the raycast hitting the ground, (2) by making the y position of the raycasthit's point the y position of the player so he sticks to the platform and (3) through quaternion.lookrotation.

The issues I'm facing:

• When not moving, player seems to be parallel to the ground but in steep angles, player starts "pumping" into the ground (collider is inside the platform)

• When moving, player is not parallel to the ground

• When moving, player doesn't mantain last faced direction, it goes back to the initial facing direction

Which would be the best way to do this, since I'm not sure if I'm aproaching this right?

I'm a beginner in c#, any kind of help would be appreciated!

 using UnityEngine;
 using System.Collections;
 
 public class PlayerMove : MonoBehaviour {
 
     Transform t;
     Rigidbody rb;
 
     public float speed;
     public float hitDistance;
 
 
     RaycastHit groundHit;
 
     void Start ()
     {
         t = GetComponent<Transform>();
         rb = GetComponent<Rigidbody>();    
     }
     
     
     void FixedUpdate ()
     {
         IsGrounded();
         Move();    
     }
 
     void Move()
     {
         transform.up = groundHit.normal;
         t.position = new Vector3(t.position.x, groundHit.point.y + t.localScale.y / 2, t.position.z);
 
         float movX = Input.GetAxisRaw("Horizontal");
         float movZ = Input.GetAxisRaw("Vertical");
         float movY = rb.velocity.y;
        
         rb.velocity = new Vector3(movX * speed * Time.deltaTime, movY, movZ * speed * Time.deltaTime);
 
         if(movX !=0||movZ!=0)
         {
             transform.rotation = Quaternion.LookRotation(new Vector3(movX,0f,movZ),Vector3.up);
         }
     }
 
     void IsGrounded()
     {
         Physics.Raycast (transform.position, -transform.up, out groundHit, t.localScale.y + hitDistance);
         Debug.DrawRay(transform.position, -transform.up, Color.red);
     }
 }