There really isn't like a 1 rule for it but you can tell if a word is en or ett by just looking at it. About 75% of the nouns are “en”. There are some rules but I would say it’s easier to just try to learn en or ett when you learn a new word. Many words for things that are alive are en, like trees, plants, animals, different professions etc. Hope this helps your sweedish studies!
Ater and äter have different pronunciations because of the sound of "ä." A typo error doesn't mean you lose any strength bars or anything, as if one was using an English keyboard, typing "ater" to someone would be understood. However, in daily speech and whatnot, "äter" is the correct spelling.
Yes, 'The man eats the apple' is Mannen äter äpplet in Swedish, but Mannen äter ett äpple can mean either 'The man eats an apple' or 'The man eats one apple'. In speech, we can hear the difference because en has a little more stress when it means 1, but in the written language you have to guess from context.
The witty pronouns and easy verb tense are making Swedish so fun to learn.