High school is correct when used as a noun.

Highschool is correct when used as an adjective (referring one who is in high school)

Cheerleader is a verb being used as a proper noun, and because this is one concept using multiple words, we mash the words together, like with High school.

Main cause of this is that German (more accurately, a predecessor to German) has a strong influence on English, and is the core of the language before it was first romanticized with the Norman conquest.

"Maybe" may be my favorite example of words we mash together

They are a single word because a highschool is not a school that is high, the 2 words being together have more meaning than themselves. I don't see how that would apply to cheerleader though, since they are quite literally leaders of the cheer.

They are separate words because a highschool cheerleader is literally that, a cheerleader of a highschool. And a highschool cheerleader captain is the captain of the cheerleaders of a highschool, no more meaning.