"'Skulle han äta surströmming'? can also mean 'Was he going to eat fermented herring'?" (1) That's how I interpreted the sentence as a native. It is depends on the context.
If you are refering to a posibility in past tense then (1) is the natural choice. "Would he eats fermented herring" would be right if you are speaking of the posibility in presence.
A more common way to ask if someone is capable of eating fermented herring is:
"Skulle han kunna äta surströmming"
which translates to
"Would he be able to eat fermented herring?"
Pickled refers to putting something in vinegar and spices, or a sauce of sorts. Fermented refers to the natural process of rotting. So it loosely translates to rotten fish. From what I understand, it is not ready to eat until the can bulges and it smells so bad they open it outside! I have only actually eaten sill in a variety of sauces.
What a culinary delight! Rotten fish!! I've only ever had pickled or smoked. In Holland I had the "zuure hareng broodje" (I think that is right.) And in Kiel, smoked but cold (not so great to my taste). The typical image is of a person holding the whole fish up above one's head, and I assume, devouring it whole. Really?
"Zure haring" is pickled in vinegar and sold in glass jars; if I am not mistaken they are without bones ("rolmops"). The herring sold on the market stalls is "zoute haring"; these can be eaten by the tail, with or without a chopped onion. I prefer "zoute haring" on bread without onions, but I hate the bones.
As an Enlishman working for a Swedish Co I have eaten and enjoyed surströmming. However I was quite clear that our Swedish hosts who had been challenging us to eat it really didn't want to themselves, when I virtually dared them to. The restaurant we went to put us in a separate cabin for the surströmming. I have to say not many shared my enjoyment!