How to Activate Random GameObjects? (C#)

Without a look at the script I'm not sure how much this will help but I'll have a go. If your pool is an array/list of GameObjects you could use Random.Range() to find a random element: objectPool[Random.Range(0, objectPool.Length)]. If you only want one active object at a time you could then store a reference/index for the current active object so that you can deactivate the current and activate a new GameObject:

     public GameObject[] objectPool;
     private int currentIndex = 0;
 
     public void NewRandomObject()
     {
         int newIndex = Random.Range(0, objectPool.Length);
         // Deactivate old gameobject
         objectPool[currentIndex].SetActive(false);
         // Activate new gameobject
         currentIndex = newIndex;
         objectPool[currentIndex].SetActive(true);
     }

Now to make this happen every 10 seconds you could monitor time yourself in an update, use a Coroutine or you can use Monobehaviour's InvokeRepeating. Here's a super quick example of a timer in update:

     float elapsedTime = 0f; // Counts up to repeatTime
     float repeatTime = 10f; // Time taken to repeat in seconds
 
     private void Update()
     {
         elapsedTime += Time.deltaTime;
         if (elapsedTime >= repeatTime)
         {
             // Do something here
             ...
             // Subtract repeat time
             elapsedTime -= repeatTime;
         }
     }

I hope some of that was useful. =)