Some problems with handmade basic player controller

I tried to make this script for some basic movements and I have some problems.

Player class:

 using Assets.Scripts;
 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class Player : MonoBehaviour
 {
     public float InputDelay = 0.1f;
     public float VerticalMovementVelocity = 12f;
     public float HorizontalMovementVelocity = 12f;
     public float VerticalRotationVelocity = 12f;
     public float HorizontalRotationVelocity = 12f;
     public float FallingVelocity = 5f;
 
     private Rigidbody Rigidbody;
     public GameObject PlayerCamera;
 
     private float VerticalMovementInput = 0f;
     private float HorizontalMovementInput = 0f;
     private float VerticalRotationInput = 0f;
     private float HorizontalRotationInput = 0f;
 
     // Start is called before the first frame update
     private void Start()
     {
         Rigidbody = Helper.GetComponentOrThrow<Rigidbody>(this);
     }
 
     // Update is called once per frame
     private void Update()
     {
         GetInput();
     }
 
     private void FixedUpdate()
     {
         Walk();
         Turn();
     }
 
     private void GetInput()
     {
         VerticalMovementInput = Input.GetAxis("Vertical");
         HorizontalMovementInput = Input.GetAxis("Horizontal");
         VerticalRotationInput = Input.GetAxis("Mouse Y");
         HorizontalRotationInput = Input.GetAxis("Mouse X");
     }
 
     private void Walk()
     {
         if (IsVerticalMovementRequested() && IsHorizontalMovementRequested())
         {
             ExecuteVerticalAndHorizontalMovement();
         }
         else if (IsVerticalMovementRequested())
         {
             ExecuteVerticalMovement();
         }
         else if (IsHorizontalMovementRequested())
         {
             ExecuteHorizontalMovement();
         }
         else
         {
             Rigidbody.velocity = Vector3.down * FallingVelocity;
         }
     }
     private void ExecuteVerticalAndHorizontalMovement()
     {
         Rigidbody.velocity = new Vector3(HorizontalMovementInput * HorizontalMovementVelocity, -1 * FallingVelocity, VerticalMovementInput * VerticalMovementVelocity);
     }
     private void ExecuteVerticalMovement()
     {
         Rigidbody.velocity = new Vector3(0, -1 * FallingVelocity, VerticalMovementInput * VerticalMovementVelocity);
     }
     private void ExecuteHorizontalMovement()
     {
         Rigidbody.velocity = new Vector3(HorizontalMovementInput * HorizontalMovementVelocity, -1 * FallingVelocity, 0);
     }
     private bool IsVerticalMovementRequested()
     {
         return Mathf.Abs(VerticalMovementInput) > InputDelay;
     }
     private bool IsHorizontalMovementRequested()
     {
         return Mathf.Abs(HorizontalMovementInput) > InputDelay;
     }
 
     private void Turn()
     {
         if (IsVerticalRotationRequested() && IsHorizontalRotationRequested())
         {
             ExecuteVerticalAndHorizontalRotation();
         }
         else if (IsVerticalRotationRequested())
         {
             ExecuteVerticalRotation();
         }
         else if (IsHorizontalRotationRequested())
         {
             ExecuteHorizontalRotation();
         }
         else
         {
             Rigidbody.rotation = Quaternion.identity;
         }
     }
     private void ExecuteVerticalAndHorizontalRotation()
     {
         ExecuteVerticalRotation();
         ExecuteHorizontalRotation();
     }
     private void ExecuteVerticalRotation()
     {
         PlayerCamera.transform.Rotate((VerticalRotationInput * VerticalRotationVelocity), 0, 0);
     }
     private void ExecuteHorizontalRotation()
     {
         transform.Rotate(0, (HorizontalRotationInput * HorizontalRotationVelocity), 0);
     }
     private bool IsVerticalRotationRequested()
     {
         return Mathf.Abs(VerticalRotationInput) > InputDelay;
     }
     private bool IsHorizontalRotationRequested()
     {
         return Mathf.Abs(HorizontalRotationInput) > InputDelay;
     }
 }
 

Problems noticed:

1) If player falls on the ground, player movements become rotations

2) Even if I ask on rotations to stay with a Z equal to 0 it still changes

Thank you for helping me