Transitions between scenes upon button press + carry over items.

If you post a code snippet, ALWAYS USE CODE TAGS:

How to use code tags: Using code tags properly

For fading, this is the approach I always use because it is so dead simple. NEVER use coroutines for fading.

Fading, simple and easy:

To keep game state from scene to scene, you need what is traditionally called a GameManager. Tons of youtube tutorials to read more about that, but here’s some simple starting points:

ULTRA-simple static solution to a GameManager:

OR for a more-complex “lives as a MonoBehaviour or ScriptableObject” solution…

Simple Singleton (UnitySingleton):

Some super-simple Singleton examples to take and modify:

Simple Unity3D Singleton (no predefined data):

Unity3D Singleton with a Prefab (or a ScriptableObject) used for predefined data:

These are pure-code solutions, DO NOT put anything into any scene, just access it via .Instance!

If it is a GameManager, when the game is over, make a function in that singleton that Destroys itself so the next time you access it you get a fresh one, something like:

public void DestroyThyself()
{
   Destroy(gameObject);
   Instance = null;    // because destroy doesn't happen until end of frame
}

There are also lots of Youtube tutorials on the concepts involved in making a suitable GameManager, which obviously depends a lot on what your game might need.

OR just make a custom ScriptableObject that has the shared fields you want for the duration of many scenes, and drag references to that one ScriptableObject instance into everything that needs it. It scales up to a certain point.