Well, first 「もらう」 doesn't not really mean "receive the favor..." as you translated it, but it means most of the time "get...". A lot of times, "get" is the most accurate translation you can get for 「もらう」, some examples:
一口もらっていい？ = can I get a bite? (to eat) or can I take a bite?
もらったカードを使って。 = Use the card you got.
彼にやってもらったことをちゃんと思い出して。 = Just remember the things you got him doing
I am not a translator but what you want to be doing learning a language is not perfectly translating into your mother tongue (which is useless if you don't want to become translator), but write literal translation which will help you understand the real logic of japanese through your mother tongue.
So you should not be worried about weird translations because the "logic of japanese language" is very different than english's.
Anyway, if there is a word you could think of as "do a favor...", it is 「～くれる」, because the one who does the action of 「くれる」 is a third person that does something (or gives something) to you/your circle:
彼がやってくれたこと。 = The things he did for me.
彼がやったこと。 = The things he did.
Anyway to sum it up, 「もらう」 does not have imply a "favor" or something, just the fact that you get something, or someone to do an action:
友達のいちばん好きな言葉を書いてもらいましょう。その読み方と意味を質問してください。 = Let's get (them?) write their friends' most liked word. And ask them the meaning and reading.