How to rotate an object around a player when pushing a button..?

Hello,

Im trying to write a code where a blueCube rotates around a redCube horizontally when pushing the left and right arrow keys and vertically when pushing the up en down keys. neither of them have rigidbodies. I created the code down below, and it seems to work fine if I use them individually. But If I combine them The blueCube does not fully rotate around the redCube, but makes circles beside it (hopefully you understand what I mean, kinda hard to explain^^). So my questions are:

a. How can I make it that the rotation does work like the blueCube Rotates the redCube the right way?

b. How can I make it so that the blueCube can not sink in the ground when moving it vertically (the -y axis relative to the position of the redCube)?

Many Thanks for helping me out!

My code:

 using UnityEngine;
 using System.Collections;
 
 public class BlueCubeMovement : MonoBehaviour {
     public Transform redCube;
     public float moveSpeed;
     private float inputVertical;
     private float inputHorizontal;
     private float movementVertival;
     private float movementHorizontal;
 
     void Update ()
     {
         float inputHorizontal = Input.GetAxis("RotateHorizontalBlue");
         float movementHorizontal = inputHorizontal * moveSpeed * Time.deltaTime;
         transform.RotateAround(redCube.position, Vector3.up, movementHorizontal);
 
         float inputVertical = Input.GetAxis("RotateVerticalBlue");
         float movementVertical = inputVertical * moveSpeed * Time.deltaTime;
         transform.RotateAround(redCube.position, Vector3.forward, movementVertical);
     }
 }