"I have not finished the homework yet."
Note that the way Duo explains Japanese present continuous is not entirely correct. The English "-ing" is not exactly equal to ～ている.
For transitive action verbs like 食べる or 読む, ～ている form just means continuous action - i.e. "I am eating" = 食べている.
But for intransitive stative verbs (like 終わる here) it means state of being. Not that "something is ending". What it actually means is that the state continues to the present, i.e. "it is finished / it is not finished".
終わる - to be finished
終わらない - it won't be finished / won't end
終わっていない - it's not finished (yet)
終わっている - it's finished
終わった - it ended
Rule of thumb: if a verb expresses something that cannot be in continuous state (i.e. 終わる), its ～ている form means state-of-being, not continuous action.
There are caveats, though, since some Japanese verbs are not considered action verbs, in sharp contrast to other languages. For example 来る. 田中さんが来ている doesn't mean that Tanaka is on his way, it means he's already here, "he's come".
No, because it means "I will not finish..."
Contrary to the weird Japanese that's being taught here, the usual way to say this is in the past tense: まだおわらなかった. To make it less plain and more polite you say, "まだ終わらなかったのです。" Some of you may be wondering about the ～ます thing, but in truth, it just isn't used nearly as much as you are being taught. Japanese as a foreign language is its own weird little dialect.
You are.... Not correct. です/ます is reeeeally common. Among friends/young people? Not as much. With colleagues, strangers, shop employees, and others you'll encounter while working or traveling there? Very common. Also, part of why they use ている form here is because they're trying to teach it. The language learning process doesn't include an automatic jump from not knowing to using perfectly common, natural sentences. You get these stiff, awkward sentences in the middle point to help you learn new forms. Then as you progress, you can develop a more nuanced understanding of when to use them.
Could this also mean "i am not finishing homework yet"? As in, i am not eating, maybe I'll finish it later.
I kind of expected this sentence to use the past tense, e.g. owarimasendeshita. The present tense confuses me a bit. I know imasen refers to the homework's present status of not finished, but i guess my question is if there is a difference between the status of being done and the status of getting done.
I don't think so.
This sentence is literally "The homework is not finished yet." Japanese frequently prefers to tell negative things like not doing, refusing requests etc. in a more roundabout way. Besides, I think the simple present/future tense would work better for your sentence.