Oh good, I was beginning to wonder if you could only speak of cookies in the plural in Polish :P
If anything, "cake, as well as cookie". The fact that your variety of English uses 'cake' doesn't change the fact that others (I guess most) use 'cookie'.
But as it is used so, then it has to be added, which I have just done.
This was in the plural lessons and has no plurals at all umm... (｡ŏ﹏ŏ)
I found this sentence in a lesson of the skill "Plurals". I think it should not be there, I do not see any plurals in it.
In English, the usage of 'a' and 'an' depends on the first sound of the word that comes after. If the first sound is a consonant, you use 'a', if the first sound is a vowel, you use 'an'. Remember that it is dependant on the pronunciation, not necessarily on how the word is written.
Because "duck" needs an article before it for the sentence to be grammatical.
Well, not exactly interchangeable as they mean different things, but in 99% of the Polish Duolingo sentences they are correct translations. "a duck" is in the main, starred answer, and "the duck" is just accepted, which makes me think that perhaps you had a typo somewhere - the algorithm then corrects you to the starred answer, which sometimes makes one think that some word was wrong.
Most probably, "they eat" and "they are eating" are accepted in every sentence with "jedzą".