Learn French: Le prince tua le monstre auquel la sorcière parla. - The prince killed the monster to which the witch spoke.

They are in the passé simple (historic past), a literary tense you will mostly see in books and written stories. For regular -er verbs like tuer (to kill) and parler (to speak), forming the 3rd person singular (he, she, or it) is very easy to spot: you just drop the -er and add an -a.

Why use auquel here instead of a simpler word like que or qui?

The verb parler requires the preposition à when you mean "speak to" (parler à quelqu'un). To say "to which" or "to whom", we must combine à with the relative pronoun lequel. Because le monstre is masculine singular, à and lequel contract into the single word auquel.

If I wanted to say this exact sentence in everyday spoken French, how would it change?

In regular conversation, the passé simple sounds strangely old-fashioned, so you would use the passé composé instead. The sentence would become: Le prince a tué le monstre auquel la sorcière a parlé.

Is monstre always masculine, even if the monster was female?

Yes, un monstre is a masculine noun regardless of the actual gender of the creature being described. That is why the sentence uses the masculine relative pronoun auquel to refer back to it, even though a female witch is interacting with it.