"Arriver" does not usually require a placeholder subject. That's just one possible usage of this verb, and not even the most common.
You can use this construction with many different verbs. I don't know about any list of them but the most frequent are "être" (be), "pleuvoir"(rain), "falloir"(must), "faire"(do), and pronominal verbs (like "se trouver", "s'imposer", "se passer"...) As far as I know "falloir" and "chaloir" (a rare verb meaning "to care") are the only ones that require a placeholder subject.
These verbs would be called "impersonal verbs" in English, but in French this is not a clear fixed category as most verbs in it could also be used without a placeholder. For example:
Les flèches pleuvent sur l'armée. / It is raining arrows on the army.
About the verb "arriver" whether it translates into "to arrive" or "to happen" in English doesn't change its French grammar. Actually as a French to me it's hard to know how to translate "arriver" depending on the context.
À propos de prof de polonais, il en arrive une nouvelle, aujourd’hui, d’où l'animation dans la classe.
is correct, but I would remove this weird comma before "aujourd'hui":
À propos de prof de polonais, il en arrive une nouvelle aujourd’hui, d’où l'animation dans la classe.
You could definitely hear that in France (as long as you are among people who care about speaking correctly).
You could also have used:
À propos de prof de polonais, une nouvelle arrive aujourd’hui, d’où l'animation dans la classe.
You get the same meaning but it's slightly less precise since it's not explicitly stated that "une nouvelle" is a teacher. It's still pretty easy to guess it given the context.