Animations Bad Scripting | Controller Script Buggy | Collider Problem | Beginner Here!

I'm make a game with a first person player with a body (for multiplayer)... There are several animations assigned to the character but it does not what I want! If I press nothing: idle Works :) If I press "Z" (forward on azerty): walk Does not work :( If i press "Z" + LeftShift: run Does not work :( If i press space: jump Does not work!!!! :(

 // Use this for initialization
 void Start ()
 {
     anim.Play("idle");
 }
 
 // Update is called once per frame
 void Update () {
     if ((Input.GetKey(KeyCode.Z)) && shiftcheck == false)
     {
         anim.Play("walk");
     }
     else
     {
         if (shiftcheck == false)
         {
             anim.Play("idle");
         }
     }

     if ((Input.GetKey(KeyCode.Z)) && (Input.GetKey(KeyCode.LeftShift)))
     {
        anim.Play("run");
        shiftcheck = true;
     }
     else
     {
         shiftcheck = false;
         anim.Play("idle");
     }
     if (Input.GetKeyDown(KeyCode.Space))
     {
         anim.Play("jump");
     }
     else
     {
         anim.Play("idle");
     }
 }

}

Also: The default controller scripts are buggy. But i don't know how to make one my self! Also: I have a flat box collider in my map but when a player walks on it he moves automaticly forward and can't control his movement any longer! Why is that?