need some help to change a player script

I’m using an asset which has a locomotion script to move the player. Unfortunately this script works the way that the player is walking in the direction where the mouse is pointing. I would like to change it so that I can use it without the mouse. The left and right arrow keys shall give the direction instead. But for some reason I don’t manage that.

This is the original script

using System.Collections;
using System.Collections.Generic;

[RequireComponent(typeof(Animator))]

//Name of class must be name of file as well

public class LocomotionPlayer : MonoBehaviour
{

    private Transform mountPoint;
    private Vector3 moveDirection = Vector3.zero;//player's move direction
    protected Animator _animator;
    private CharacterController _charCtrl;
 
    private bool _jump;//jump button press detection
 
    public bool _run;
    public bool canRotate = true;
    public bool holding;
    public bool alive = true;
 
    public float _speed;
    public float _strafe;
    public float gravity;//gravity force
    public float health;

    private float _mouseX;
    private float tapTimeWindow;

    public int tapCount;

    // Use this for initialization
    void Start ()
    {
        _animator = GetComponent<Animator>();
        _charCtrl = GetComponent<CharacterController>();
        m_AudioSource = GetComponent<AudioSource>();
    }

    void Update ()
    {
        _mouseX = Input.GetAxis("Mouse X");
        _speed = Input.GetAxis("Vertical");//reading vertical axis input
        _strafe = Input.GetAxis("Horizontal");//reading horizontal axis input
        _run = Input.GetKey(KeyCode.LeftShift) ? true : false;//check if run button was pressed
        //PROCESSING ROTATION
        Vector3 aimPoint =  Camera.main.transform.forward * 10f;
        if (canRotate)
        {
            Quaternion targetRotation = Quaternion.LookRotation(aimPoint);
            this.transform.rotation = Quaternion.Slerp(transform.rotation, targetRotation, 4 * Time.deltaTime);
            this.transform.rotation = Quaternion.Euler(0, transform.rotation.eulerAngles.y, 0);
        }


     
        if ((_charCtrl != null) && (!swimming))
        { //is character controller enabled 
            if (_charCtrl.isGrounded)
            {
                moveDirection.y = 0;
            }

        }
     
    }
    void FixedUpdate ()
    {
        _animator.SetFloat("mouseX", _mouseX, 0.3f, Time.deltaTime);
        _animator.SetFloat("Speed", _speed);
        _animator.SetFloat("Strafe", _strafe);
        _animator.SetBool("Run", _run);
        _animator.SetBool("JumpOverObstcle", _jumpOverObstcle);
        _animator.SetBool("holding", holding);
        _animator.SetInteger("SwingCount", tapCount);
     
    }
 
}

I changed it to:

using UnityEngine;
using System;
using System.Collections;
using System.Collections.Generic;

[RequireComponent(typeof(Animator))]

//Name of class must be name of file as well

public class LocomotionPlayer : MonoBehaviour
{

    private Transform mountPoint;
    private Vector3 moveDirection = Vector3.zero;
    protected Animator _animator;
    private CharacterController _charCtrl;
 
    private bool _jump;
 
    public bool _run;
    public bool canRotate = true;
    public bool holding;
    public bool alive = true;
 
    public float _speed;
    public float _strafe;
    public float gravity;
    public float health;

    private float _mouseX;
    private float tapTimeWindow;

    public int tapCount;

    // Use this for initialization
    void Start ()
    {
        _animator = GetComponent<Animator>();
        _charCtrl = GetComponent<CharacterController>();
        m_AudioSource = GetComponent<AudioSource>();
    }

    void Update ()
    {
      _mouseX = Input.GetAxis("Horizontal"); // -->> Changed here
        _speed = Input.GetAxis("Vertical");
        _strafe = Input.GetAxis("Horizontal");
        _run = Input.GetKey(KeyCode.LeftShift) ? true : false;
        //PROCESSING ROTATION
        Vector3 aimPoint =  transform.forward * 10f; // -->> Changed here and removed if statement

      

        Quaternion targetRotation = Quaternion.LookRotation(aimPoint);

        this.transform.rotation = Quaternion.Slerp(transform.rotation, targetRotation, 4 * Time.deltaTime);

        this.transform.rotation = Quaternion.Euler(0, transform.rotation.eulerAngles.y, 0);

 


     
        if ((_charCtrl != null) && (!swimming))
        { //is character controller enabled 
            if (_charCtrl.isGrounded)
            {
                moveDirection.y = 0;
            }

        }
     
    }
    void FixedUpdate ()
    {
        _animator.SetFloat("mouseX", _mouseX, 0.3f, Time.deltaTime);
        _animator.SetFloat("Speed", _speed);
        _animator.SetFloat("Strafe", _strafe);
        _animator.SetBool("Run", _run);
        _animator.SetBool("JumpOverObstcle", _jumpOverObstcle);
        _animator.SetBool("holding", holding);
        _animator.SetInteger("SwingCount", tapCount);
     
    }
 
}

Now my player is walking left and right when I press the left and right arrow keys but he isn’t doing it while he is walking forward, he only does it while he stands still. What do I do wrong?

Ok I tried some more today. Now my player ist walking to the left and right while he is walking forward but he doesn’t turn the body to the left or right during the walking. I have no idea what’s wrong and hope someone can help me:

void Update ()
    {
        if (Input.GetKey (KeyCode.LeftArrow))
            _mouseX = -1f;

        else if (Input.GetKey(KeyCode.RightArrow))
            _mouseX = 1f;
        else
            _mouseX = 0f;

       
        _speed = Input.GetAxis("Vertical");//reading vertical axis input
        _strafe = Input.GetAxis("Horizontal");//reading horizontal axis input
        _run = Input.GetKey(KeyCode.LeftShift) ? true : false;//check if run button was pressed
        //PROCESSING ROTATION
        Vector3 aimPoint =  transform.forward*10f;
       

         Quaternion targetRotation = Quaternion.LookRotation(aimPoint);
         this.transform.rotation = Quaternion.Slerp(transform.rotation, targetRotation, 4* Time.deltaTime);
         this.transform.rotation = Quaternion.Euler(0, transform.rotation.eulerAngles.y, 0);
        
}