Learn Portuguese (Portugal): Os diretores da escola são simpáticos.

The singular word is diretor, which ends in the consonant -r. In Portuguese, when a noun or adjective ends in -r or -z, we add -es to make it plural.

Why does the sentence use da escola instead of de escola?

da is a required combination (contraction) of the preposition de (of) and the feminine article a (the). Together, they mean "of the school".

Why does simpáticos end in -os when the word right before it, escola, is feminine?

Adjectives always match the noun they actually describe, no matter where they sit in the sentence. Here, simpáticos (nice) describes Os diretores (the masculine, plural directors), not the school.

Why do we use são instead of estão for "are" in this sentence?

We use são (from the verb ser) because being nice (simpáticos) is being described as a permanent personality trait of the directors. If we meant they were just acting nicely in this specific moment, we would use estão.