Learn Turkish: Kadınlar eski otelden şikâyet etti mi? - Did the women complain about the old hotel?

This is the core of your current lesson! In Turkish, certain verbs always require the ablative case (-den or -dan). The verb şikâyet etmek (to complain) is one of them. You always complain "from" something in Turkish, so "about the hotel" becomes otelden.

The subject is plural (kadınlar), so why isn't the verb plural (ettiler)?

In Turkish, when a human subject is explicitly stated and already has a plural ending (-lar or -ler), the verb can just stay in the singular form (etti). While ettiler would also be perfectly correct here, dropping the plural on the verb is very common and natural.

How does the verb şikâyet etti work?

It is a compound verb made by combining the noun şikâyet (complaint) with the helper verb etmek (to do / to make). Turkish uses etmek or yapmak with many borrowed nouns to turn them into actions. So literally, this means "made a complaint".

Could I place the question particle mi somewhere else in this sentence?