донька here sounds with an accent on 'a' - like донькА. Isn't right to say дОнька?
Yep, дОнька is standard Ukrainian, but донькА is regional and quite common.
I don't understand what is meant by ь "softening" the previous letter. он would usually make a sound like "on" but here sounds more like "oyn." How is yn a "softer" version of n?
There is a good advice to compare "н" and "нь" with "n" and "ñ" in Spanish. Ukrainian "ь" also softens the other letter like this.