It depends on the gender of the word. Technically there are three genders: feminine, masculine, and neutral, although the feminine is rarely used in bookmål and can be replaced with the masculine form. Some places replace the "ei" with "en", but replace the "-a" ending, it just depends on the dialect.

Feminine: "ei" / "-a" Example: "Ei ku" / "kua" Masculine: "en" / "-en" Example:"En stol" / "stolen" Neutral: "et" / "-et" Example: "Et hus" / "huset"

I think one is the neuter, maybe?

There is no difference. the and a are the same thing they use different words on how ur saying it

Yes, they are treated as synonyms.

Apparently, it is also related to Old High German which was also "barn", "bearn" was the Old English word which also gave rise to the verb "bear".
http://www.merriam-webster.com/dictionary/bairn http://www.oxforddictionaries.com/definition/english/bairn

You do need to bring your lips together in order to form the correct sound. IPA pronunciation is /bɑːɳ/. Follow this link to listen how a native speaker pronounces this word.

Click here to find out more about these symbols.

• befriend a Norwegian
• record yourself saying the word (use www.forvo.com to find the word and then compare the two)
• pay someone to teach you Norwegian
• visit this link if you own a microphone of some kind

No, because "the girl" (definite article) is jenta, but "a girl" (indefinite article) is en jente.

Biological gender and grammatical gender aren't one and the same.

Both nouns in this sentence have grammatical genders in Norwegian. Every noun is either masculine, feminine or neuter in Norwegian.

En jente is masculine (ei jente [feminine] is rarely used) and et barn is neuter.