How to make a 2D object, which can be moved left and right, constantly fall downwards?

Just add a Rigidbody2D component to the gameobject then set its "Gravity Scale" to a really low number to make it fall slower. It falls slower because it's being affected less by gravity the lower its "Gravity Scale" is. In addition to falling down, if you want to move the object to the left and right, just add a script with this code to the object.

 using UnityEngine;
 using System.Collections;
 
 public class Player : MonoBehaviour {
     public float speed = 2f;
 
     Rigidbody2D rigidbody2d;
 
     void Awake () {
         rigidbody2d = GetComponent<Rigidbody2D> ();
     }
 
     void FixedUpdate () {
         if (Input.GetKey (KeyCode.LeftArrow))
             rigidbody2d.velocity = new Vector2 (speed * -1, rigidbody2d.velocity.y);
         if (Input.GetKey (KeyCode.RightArrow))
             rigidbody2d.velocity = new Vector2 (speed, rigidbody2d.velocity.y);
     }
 }

All this is doing is grabbing the Rigidbody2D component at the beginning of the game, then just changing its velocity based on what the player's pressing on the keyboard. You can even change how fast it moves left and right by changing the speed variable in the inspector.