"Did you finish your homework?"
Japanese sometimes has pairs of verbs with very similar meanings (in fact, they use the same root kanji); they are distinguished by whether the action is performed by an agent (transitive) or not (intransitive). When you use an intransitive verb, you cannot use を; you must use a different particle.
The sentence above uses 終わる (おわる), which is an intransitive verb; it cannot take a direct object. An overly literal translation of the above might be, "as for homework, finished?" You could also use が instead of は here, which might be more like "homework finished?"
There is a transitive verb 終える (おえる) -- which uses the same kanji! -- that also means end/finish, and can take a direct object. So you could also express this as しゅくだいをおえましたか?
Note that, in English, verbs are often both transitive and intransitive ("I opened the window" vs. "The window opened"), and this is not the same as passive voice ("The window was opened").
(This information comes from Tae Kim's excellent online grammar guide: http://www.guidetojapanese.org/learn/grammar/in-transitive )
Just by looking at the word, no, I don't think there is.
I don't know if this is common enough to be used as a rule of thumb, but I just noticed that there are a few transitive verbs that end in -eru, while their intransitive counterparts do not: Transitive: 閉める (しめる, to close something) Intransitive: 閉まる (しまる, to close)
Transitive: 開ける (あける, to open something) Intransitive: 開く (あく or ひらく, to open)
Transitive: 助ける (たすける, to save something/ someone) Intransitive: 助かる (たすかる, to be saved)
Transitive: 終える (おえる, to end/ finish something) Intransitive: 終わる (おわる, to come to an end/ be finished)
The Japanese avoid using あなた. I think Duo shouldn't be teaching students to use it, as it implies a degree of familiarity that may be odd or even presumptuous in some cases. In the four years I lived in Japan (two different roommates and a boyfriend) working in a Japanese company, I can't recall a single time someone used あなた or あなたの with me. They either used my title, or my last name + san.
I may be mistaken, but i believe i saw a sign in an American airport reading, あなたの荷物 (にもつ) をご注意 (ごちゅうい) ください (please look after your luggage) So i think it does have some use in general notices like that. It's also used by wives to their husbands (like calling them "dear")