Why is the "new" female?
Because adjective have to agree with the noun it describes – "zupa" is feminine, so the adjective takes the feminine form.
Why is smaczna nominative ? Shouldn't it be instrumental ? Or is it nominative because of the "nie" ?
It would be Instrumental if it was a noun phrase (regardless of the negation). But it's just an adjective. An adjective on its own stays in Nominative.
"Zupa jest smaczna" vs "Zupa jest smacznym jedzeniem".
are there any specific reasons "ain´t" is not accepted?
Yes, that is completely colloquial grammar and this course is after all taken also by Polish people learning English.