As for how to use them:
- deine (you are talking to a single person with whom you are on familiar terms or who is not a grown person, i.e. to a "du")
- eure (you are talking to multiple people, i.e. to "ihr")
- Ihre (you are talking to one or multiple adult people with whom you are not close and/or who is in a position of respect from your perspective, i.e. to a "Sie")
Thanks for providing some insight into the use of the terms, I forgot to do so. I'd only like to add that the polite form (Sie, Ihre) can apply to both a single person and to several persons (e.g. when addressing a couple with whom you are on formal terms: Herr F. und Frau F., es war mir eine Freude, Ihre Bekanntschaft zu machen und Ihre Kinder kennenzulernen.).
Ah right, forgot about that possibility, thanks for pointing it out! I corrected the mistake.
Kuchen = cake, kochen = to cook ;) The two sound somewhat similar but they are not actually related (Kuchen is an original Germanic word from a Proto-Indo-European word for “round, ball-shaped”; kochen is a borrowing from Latin “coquere”).
Yes, that should be accepted because the plural of Kuchen is still Kuchen.
Adding “the” would be talking about a specific cake rather than cake in general as the German sentence does. If we wanted to talk about a specific cake, we would use the definite article and say den Kuchen just like you would in English.
Today I learned that Duolingo doesn't accept "Y'all's" as a valid translation for "eure." That's how us Southerners would probably translate it... :P