"The good life"
Translation:Det gode liv
Both should be accepted now. It's a fixed phrase, but in general you should say 'det -et' or 'den -en/-a'.
Yes, I've corrected it now :)
In older texts and Danish you'll find that "Den fine utstilling" and "Den vakre jente" is more common. For some expressions this is still true, but it often sounds unnatural.