if i can ask: why do the duolingo requires articles "a" or "the" in front of the word "big"? The word "big" is enough specification of the word "mouse".
"Big mouse is eating cheese." is not a grammatically correct English sentence, you have to put either "the" or "a" (or "this" or "that"), unlike in Polish where you don't need any article.
No, it doesn't. 'A big mouse' refers to some mouse which happens to be big. 'The big mouse' refers to one specific mouse.
For example, if you were talking about your pet mice you would say 'the big mouse' because you have a specific mouse in mind (i.e. your pet mouse). I hope this makes sense.
Even if there is enough information to convey what is intended, we still have to follow the structure/rules of the language we're translating into. Thus, to translate correctly into English here, we need to add a definite or indefinite article ("the" or "a").
Given the form of the adjective, I assume mysz a feminine noun, even though it does not end with an "a." Is this an exception to the rule?
Not a real exception, just a rule you did not know.
Feminine nouns do not have to end with -a, there are many feminine nouns that end with a "soft" or "semi-soft" consonant.
I wrote a bit about genders in Polish https://www.duolingo.com/comment/14133935 and my opinion on those is :
If a word ends with ń ć, ś, ź, ż, sz, cz - you can toss a coin, or check a dictionary, it might be feminine or masculine.
I haven't had the opportunity to check thoroughly the grammar and vocabulary beyond duolingo. I still get confused by the similarities between the verb " to be" and "to eat", what are the most common conjugations of them?
I Wonder if I can find some kind Of grammar somewhere? My friend told me that there is grammar in the spanish version..
There are Tips and Notes until some point, not for the whole course. More are coming. You can access them by clicking at a skill icon and then the lightbulb icon, if you don't see it in your app, use the website version.
Also, you may find a lot of interesting topics here: https://forum.duolingo.com/comment/16296174