Why is the best translation "I am standing and cooking"? I thought that the real meaning of "står" in this sentence was grammatical, meaning the continuous form (I am doing something), not the actual standing. If one says "I am standing and cooking" the implication is that I am opposing this sentence to "I am sitting and cooking". I would appreciate your enlightening us.
You're absolutely right - plain "I am cooking" is the best and most natural translation.
However, please bear in mind that whatever we put as the default translation is what Duolingo choses for the reverse exercise - "translate into Swedish". Hence, if we put just "I am cooking" as the default, you'll be asked to translate that into Swedish, and you'll put jag lagar mat for that - which is typically better in isolation, without context.
So by putting the more idiomatic English option as the default translation, we lose the ability of teaching the idiomatic Swedish option, and thus we need to use the worse translation as the default one. It's unfortunate, but not something we can affect well.
It looks like Dutch has several (5!) ways to express the progressive tense, including the "I stand and cook" way. https://en.wikipedia.org/wiki/Continuous_and_progressive_aspects#Dutch