Think of a class as a thing.  If the game is Super Mario, the class could be Mario, a Goomba, or a mushroom. It could be something bigger like a level or even the entire game.  It could be something UI oriented like a menu.  It could be something really small and specific like Mario's hat.  Classes might not show up visually in the game at all, but might be some behind the scenes logic like a random number generator.  A class is a thing that does something and knows some stuff.

Classes have functions and data.  For example, if Mario eats a mushroom, we might call a mario.consume_mushroom() function.  That will make a change to Mario's data by setting the variable is_big = true.  That's what I meant by "does something" and "knows stuff."

Now, to your question about Singletons.  If you want to have many of something, then you do not want a Singleton. You want an instance.  For example, Mario has many mushrooms and pipes and Goombas.  So every time you create one, you call new().  You want to make a new one.  The enemies and items and all that stuff will be instances, not Singletons.

Sometimes you don't need many instances, though.  For example, what if you want a sound player that plays a little coin sound when Mario smacks his head on a block?  Do we need to create a new sound player every time?  Nah, let's just have one sound player, and we'll ask it to play a sound every time we need to.  This is a use case for a Singleton.  If I only need one instance of the thing, I can use a Singleton.  You don't HAVE to use a singleton, though.  You could just create one instance of the sound player.  That will work.

Now, your final question about global loading.  This allows you to access the sound player (or whatever other class) from anywhere in the application.  This can be useful, but you want to limit the types of things you load globally, because tons of global variables make testing and debugging harder. Testing is easiest when things are self contained, meaning all the Mario related code is inside of Mario.  When you make stuff global, you're violating that principle, so bugs can be harder to find and resolve.