Learn Italian: Fermo la macchina vicino al muro.

You use the reflexive fermarsi (like mi fermo) when you are stopping yourself or coming to a halt. Because you are stopping a separate object (the car) in this sentence, you use the standard, non-reflexive verb fermare (fermo).

Why does it say vicino al muro instead of just vicino il muro?

In Italian, the phrase for "near" is vicino a. When placed before a noun, you have to combine the preposition a with the definite article of that noun. Here, a combines with il to form the word al.

I've also learned the word parete for "wall". Could I use it here?

You could, but it would change the setting. A muro usually refers to an exterior wall, a thick structural wall, or a standalone wall outside. A parete refers to an interior wall inside a room or house. Since you are driving a car, an outdoor muro makes the most sense here.

Is there a difference between using macchina and auto for a car?

They are highly interchangeable! Macchina literally means "machine" but is the most popular everyday word for a car in spoken Italian. Auto (short for automobile) is also very common but can sound just a tiny bit more formal or technical.