How can I handle scripts correctly? What's a good way to apply scripts to GameObjects?

Hi all. I'm new to Unity. In the past 6 days, I've been reading guides, browsing the manual and watching video-guides.

I'm making a simple 2d game in Unity for school which consists of 4 mini-games. On my first mini-game, the objective is to move a character on a 2d field with the accelerometer and to pick objects in a limited timespan. A very simple game. However, there's only one thing that puzzles me: where do I apply the scripts?

They are easy to write, that's true. But what's the best way to apply them to a gameobject?

If i make a script that destroys the collectible when the player touches it and instantiates a new one in a random position, i could place this script on the player GameObject, but then if i want to do "score++" each time player touches a collectible i should keep track of the score in the player script. If i wanted the timer to reset everytime player touches an object, i should keep track of time in the player script, and so also the GameOver() function should be put in the player script. I just attached the script that handles the entire mini-game on the player object.
What if i want the playerScript to call a function from another script (and from another object)? For example:

 void OnTriggerEnter2D(Collider2D trigger)
 {
     if (trigger.tag == "Enemy")
     {
         MiniGameManager.GameOver();
     }
 }

There could be hundreds of ways to bring the game to a "Game Over", but i can't always repeat the same code. A good way for me would be to make a mini-game manager that is visible to all the scritps in the scene. How can i put this in practice, without draggin and droppin the "mini-game manager" everywhere?

Thank you in advance for your availability.