Learn Russian: Ты должен дойти до холма до вечера.

It is doing three completely different jobs! First, it's a prefix on the verb дойти, adding the meaning of "reaching a destination." Second, it's a spatial preposition in до холма, meaning "as far as the hill." Third, it's a time preposition in до вечера, meaning "before" or "until evening."

Why do the words холм (hill) and вечер (evening) both end in -а here?

They are both in the Genitive case. The preposition до always requires the Genitive case, whether you are talking about reaching a physical boundary (до холма) or a time limit (до вечера).

Why use the perfective verb дойти here instead of the imperfective доходить?

Because the sentence focuses on successfully completing a single, specific trip with a deadline ("before evening"). If you were talking about a recurring habit or the process of walking (e.g., "You must walk to the hill every day"), you would use the imperfective доходить.

How would this sentence change if I were speaking to a woman?

You would need to change должен to должна. In Russian, "must" or "have to" is often expressed with this short adjective, which has to agree with the gender of the person who must do the action: ты должен (to a male) vs. ты должна (to a female).