Learn French: Le chef a convoqué l'équipe, mais personne n'a répondu. - The boss convened the team, but no one answered.

You would say mais tous ont répondu. Because tous replaces the noun and acts as a standalone plural indefinite pronoun here (meaning "all of them"), you must pronounce its final "s" (/tus/). Contrast this with personne, which acts as a singular pronoun and takes a singular verb.

Why does personne come before the ne here? I usually see ne ... personne.

In the second half of this sentence, personne is the subject ("no one"). When it acts as the subject, the structure is personne ne followed by the verb. The standard ne [verb] personne order is only used when it is the object, as in Il n'a convoqué personne (He didn't summon anyone).

Is convoquer a false friend for "convoke"?

They share the same root, but convoquer is much more common in everyday French work and school life. It means to officially call someone in for a meeting, an interview, or to summon them to an office. It implies a sense of authority, which fits perfectly with le chef (the boss / manager).

Since an équipe is a group of people, could I ever use a plural verb with personne?

No, personne is strictly singular. Even though it refers conceptually to the multiple members of the team, the pronoun personne always takes the third-person singular conjugation (a répondu, never ont répondu). It works exactly like "nobody" in English.