"En bjørn er et dyr."
Translation:A bear is an animal.
You use 'en' for masculine nouns, 'et' for neuter words and 'ei' for feminine nouns. The difference is the noun's gender, which has to be memorized.
No, there are no such categories. The gender a noun is assigned is quite arbitrary, and will have to be memorised with each noun. It does not match up with biological gender, and the only rules that exists are for certain categories of loanwords.
I think it's somewhere between 'dur' and 'diur' but the 'i' sound would be very short and subtle. maybe wrong, waiting for a native speaker to chime in. I'm basing this on what I'm hearing and on linguistic cognates so not 100% sure.