In the audio file, it's difficult even for a native speaker to hear if it is "den" or "denne".
I agree, but I guess it is not important in everyday speech, this key or that key, so it naturally gets squished!
when 'åpne' and when 'åpen'?
(å) åpne = infinitive of the verb
åpen = adjective in singular, masculine/feminine
åpent = adjective in singular, neuter
åpne = adjective in plural, for all genders.
Hope that helped!