This requires the reflexive object, right? "Jag sätter ned på stolen." doesn't work, correct?
Quite correct. :) You're putting something on the chair, and you need to specify what. If it's yourself, you use a reflexive object.
Woo! So it really means "I set myself", and you can set something else as well.
Actually, "I seat myself" :)
If "sätter" [sig] is "sit," what is "sat"?
That would be satte [sig]. But please note that sitta means "sit" and sätta sig means "sit down", so there's a difference.
What about "Jag slår mig ner/ned på stolen"?
Is it not accepted because it's not literal? Or just a missed option?
Probably just the latter - it's a great translation. Just one thing you should note: it's mostly in the "making oneself comfortable" sense, so not exactly a phrase you'd use for someone sitting down to be interrogated.
Thank you for the answer!
btw, for whoever is interested, "slå dig ner" is one of the first sentences in Bonus Familjen, if someone wants to listen to it in a context.