Player going through walls

I know there is already a lot of similar questions out there, but none of them have any helpful answers. I have a player with a Rigidbody and a Capsule Collider. I have some simple 3D Cubes for ground and walls. When I move the player against a wall, it just glitches through. :( Here's my script:

 public KeyCode forwardKey;
 public KeyCode backwardKey;
 public KeyCode leftKey;
 public KeyCode rightKey;
 public KeyCode jumpKey;

 public float speed;

 Rigidbody body;

 // Start is called before the first frame update
 void Start()
 {
     body = GetComponent<Rigidbody>();
 }
 
 void FixedUpdate()
 {
     // Movement
     Vector3 new_pos = new Vector3(Input.GetAxis("Horizontal"), 0, Input.GetAxis("Vertical"));
     body.MovePosition(transform.position + new_pos * Time.fixedDeltaTime * speed);

     // Jumping
     RaycastHit hit;
     Vector3 down = transform.TransformDirection(Vector3.down);
     if (Physics.Raycast(transform.position, down, out hit, 1f))
     {
         if (Input.GetKeyDown(jumpKey))
         {
             body.AddForce(Vector3.up * 500);
         }
     }
 }

Also, if anybody knows why my jumping isn't working, that would be useful too.

Thanks in advance! :D