My inner translator would accept fine as a translation for fin in some cases, notably when speaking about things like fine grain, but not in others.
I asked team member cathmach who is a native speaker of English what fine really means. She said there are two meanings of fine that might fit here: 1) "superior/of very high quality/excellent" (maybe corresponding to utmärkt in Swedish), and 2) "acceptable/satisfactory/reasonably good (but no better)". Neither of those are a very good match in this sentence, so I say nay.
@later question: Swedish fin has tons of different uses, but the central one that is used most often today and that would work in a sentence like this is something between nice and pretty. (pretty might even be a better translation in this specific case)
I feel that in a sentence like this, fine in English would either mean just OK (or like, 'unharmed'), or it would be a notch over what fin really says in the Swedish sentence (and a somewhat different nuance).
If you mean 1.2. not bad, then OK is an ok translation. If you mean 1.1. 'very good', then anything meaning very good is a very good translation. For meaning 1.3, maybe snygg, tjusig (though as they describe it, this one seems to be more about people). For 1,4 or 1,6., maybe subtil (I doubt either of these would really fit in this sentence with no context). I can't see how any of the others could apply in this sentence.
I agree. When your wife/partner asks you how she looks, "fine" is likely to get a disapproving look at the very least ramping up to a full-blown slap. It is very much a throw away comment which implies you have not really considered the question. My understanding of "fin" is nice, pretty or even beautiful depending on how good she really looks!