So I'm guessing that the present form can mean "I eat" and "I am eating" since both translations are accepted
"Jag är ätandes" looks to me like a literal translation of the English progressive construction. I wouldn't consider it idiomatic Swedish. The progressive in Swedish would more naturally be Jag håller på att äta/och äter or Jag sitter och äter.
The fact that Swedish doesn't make the distinction between progessive and non-progressive, doesn't mean that the language can't express them. It simply means that you don't need to make a choice whether to do so, like in English. "Jag äter" equals both I eat and I am eating.
It's not an accent, it's a letter itself. The Swedish alphabet has three more letters than the English one, åÅ, äÄ and öÖ.
It is rather curious that in many languages "to eat" and "to am". Like "Er isst" and "er ist" in German, or "on jest" and "on je" in Polish (and Czech uses "je" as "to be") and Russian "есть" in different situations can be a variation of both (like "У тебя есть что есть?", translated to "Do you have things to eat?"). There is something philosophical here in all of that.
For anyone taking spanish, "I" in Swedish sounds a lot like "I" in Spanish to me. Would it be safe to think of the I that way?
In Danish there is a distinction between "spiser" og "æder" to name the action of eating. "Spiser" is used for humans and it's civilized, while "æder" is used for animals or very informal/uncivilized for humans or sometimes as an insult towards one that stuffs his/her face like an animal. There is no such thing in English, as "to eat" is universal and with no implications. Is there the same distinction in Swedish?
While "I eat" can be translated to "Jag äter", "Jag äter" is referring more to the act itself, where "I eat" doesn't quite make sense.
"I am eating" is more accurate to describe the act itself.
Sidenote: "Jag äter frukost" (for example) would best translate as "I am having breakfast"