The following is true for the Oslo dialect, but different dialects handel these silent letters differently.
In "and", the d is silent, so you pronounce it "an". In "anden", the d and the e are both silent, so you pronounce it "an'n", or "ann". If you pay really close attention you might be able to hear it.
My Norwegian roommate said "When in doubt, just pronounce all the letters, and people will be ok with that". You can also pick up which one is which from context of the sentence.
It almost sounds like the voice audio is that computer generated speech rather than a person. Sometimes it's near impossible to distinguish what she's saying.
I may be wrong, but I think it is a matter of grammar: I haven't met nouns without an article in Norsk yet (except for names of course),so if you meet smth like "An", it must be "the duck" and if it is "en an", it is "a duck".
And, surely, changing language to an easier one is the worst way to learn it. It is like making friends with somebody. You either accept him or her with all his or her madness, or give up communication at all.