It would really help if duolingo gave us an indicator of case as we go - so we know either which case we are in, or after our answer which case we were supposed to be in. I appreciate case can change within a sentence.
Well, there isn't really a place to put it, no place to put explanations in.
Here, you just have a noun phrase (well, two noun phrases), not anything in a sentence. Therefore you should use Nominative, as you treat it like something in a dictionary.
How am I supposed to know, if we are talking about one or more mothers and fathers? I know it says "your", as in belonging to more than one person, bit these persons could be siblings, and in that case, wouldn't it be the exact same sentence, but meaning just one of each type of parent?
If they shared the same mother, you wouldn't say "your mothers" - "wasze matki", you'd say "your mother" - "wasza matka". So if you wanted to talk something about the mother and father of a group of siblings, you'd say "wasza matka, wasz ojciec".
Wasze is plural Yours (more than one owner) reffering to a singular Neuter noun OR to a plural noun that is either Feminine, neuter or masculine (not personal tho, i.e. a dog). Wasi is the plural Yours for a plural masculine personal noun. And both Wasze and Wasi are have same spelling in accusative and nominative. So you have it easier at remembering it. I hope this helps.
Your mum, your dad should have been accepted as a translation.... in New Zealand we rarely refer to a parent as mother and father too formal.
I'm still not hearing the difference between ę , e , and y and e endings...and yes I know I should know which ending by the case...but still.
Well, if it's the final sound of the word, most native speakers will pronounce -ę exactly the same way as -e, or nasalize it just a bit.
As for y/e, I'm afraid you just have to listen more... they are different.