Swedish dont make a difference between the present simple and the present continous?
går has both the general meaning of "go" and the meaning of "walk". I would not usually translate "walk" as promenera, unless I meant "take a stroll".
Yes, there is no such form in Swedish. In English you distinguish between continuous (I am walking) and present (I walk) but we use the present tense for both these.
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It sounds like she is pronouncing the "g" at the end of "jag," when in other places it is not pronounced. Is there a rule or explanation of why that is?
I hear only one g as first letter in word går. Maybe you misheard and concluded that.