Learn Dutch: Iedereen heeft een mening. - Everyone has an opinion.

Just like the English word "everyone", the Dutch word iedereen is treated as a grammatically singular subject. Therefore, it takes the singular verb form heeft (has).

Could I use allemaal instead of iedereen in this sentence?

No, because they are used differently in a sentence. Iedereen acts as the standalone subject meaning "everyone" or "everybody". Allemaal means "all" or "all of them" and needs to be paired with a plural pronoun. For example, you could say Zij hebben allemaal een mening (They all have an opinion), but you cannot start the sentence with allemaal.

Is mening a de word or a het word?

It is de mening. A very handy rule to remember is that almost all Dutch nouns ending in -ing are de words.

I know the verb bedoelen means "to mean". Is that related to the noun mening?

Not quite! Mening comes from a different verb, menen, which translates to "to suppose," "to believe," or "to mean" in the sense of being serious or genuine. Bedoelen is used when you are trying to explain what you signify or intend (like asking someone "What do you mean by that?").