Well, you have two different things going on. There's the simple indefinite article which is et for neuter, ei for feminine, and en for masculine. Then, each of those is intensified, as it were, to mean a quantity of one. For et, a second t is added: ett. For ei and en, an acute accent is added to the e: éi and én.
It looks like "en" can mean "a", "an", "one"..., but " én" can only mean "one". http://www.norskengelskordbok.com/en/dictionary-norwegian-english/%C3%A9n
one (ha..) word emphasizes whatever comes after. I have one cat vs I have a cat. One puts emphasis on that part of the sentence it just clarifies that you have ONE cat. Most of the time A/(an) is acceptable but if you must clarify how many then ofc you use one. I want a muffin vs I want one muffin is a good example although as an american whenever I order something I do tend to use a instead of one but I dont think thats correct of me
Only if you meant a girl in general i presume. Imagine you had five girls, at a burger joint, four have eaten. You wouldn't say "a girl is eating", it would grammatically sound better, personally, to say "One girl is eating, the others are not..." Could be wrong lol
The é doesn't exist in the alphabet but that doesn't mean it doesn't exist in the language. See Italian. You only have "E" in the alphabet, but you do use both é and è as the situation requires.. Same for Norwegian. Also keep in mind that many people we know don't use the correct grammar on a daily basis, but that doesn't mean that a correct grammar does not exist just because people don't use it