Learn French: Le maire travaille à la mairie. - The mayor works at the town hall.

Yes, they do! The words maire (mayor), mère (mother), and mer (sea) are all pronounced exactly the same way in French. You have to rely on the context of the sentence to know which one is meant.

Can I say la maire if the mayor is a woman?

Historically, le maire was always masculine regardless of who held the office. However, in modern French, it is perfectly normal and very common to say la maire when referring to a female mayor.

Why do we use à la mairie instead of dans la mairie to mean at the town hall?

We generally use à (and its forms like à la or au) for public places and institutions when talking about their function or general location, just like saying at the town hall in English. You would only use dans la mairie if you specifically wanted to emphasize being trapped or standing physically inside the building.

Are maire and mairie related words?

Yes, mairie (town hall) is built directly from the noun maire (mayor) by adding the ending -ie. This ending often indicates a place, state, or concept in French (similar to -y or -ery in English). So a mairie is quite literally the place of the mayor.