My god. Why the f**k did people dislike this comment? What is so offensive in it?

It is Nominative, but you can tell only from the case "wino" has, and the function they have in sentence- subject. "Jej" does not change with cases, ("jego" -his, its and "ich"-their also do not change )

I do not know for sure, but let's translate a dictionary :

1) dobry pracownik - a good worker - The one that is just like they should be or are expected to be and thus positively seen/graded./judged by the speaker

2) dobry uniwersytet, dobry ród a good university, a good family/house - the one that is high quality or is high in hierarhy

3a) dobry człowiek - good man/human/person - the one that is kind/friendly, acts fairly and justly

3b) dobry charakter- good character/personality/nature - the one that is characteristic for the person that is kind/friendly, acts fairly and justly

4 dobry znajomy - good acquaintance ( good mate) - one that you are in close relationship

5 dobry okres - good period (of time) - one in that has more positive aspects

6) dobra opinia - good opinion/reputation - the one that contains approbation

7) dobry kawałek drogi - ( literally good piece/bit of road/way - a long way ) - having the amount that the speaker sees as considerable.

I think the number 3 can be translated to kind sometimes

No. You don't put your subject into instrumental case. Subject is always in nominative case, it's what we need nominative case for =). You normally put only objects and related modifiers in instrumental case.

These are grammar notes. If you encounter them in the puzzle exercise, just ignore them.