Questions & Answers about Hann var án hjálms en hann var með húfu.
Why does the word for helmet end in -s here (hjálms)?
The preposition án (without) is one of the special prepositions that force the noun following it into the genitive case. The dictionary form is hjálmur (a masculine noun), and its genitive form drops the -ur and adds an -s, becoming hjálms.
Since án takes the genitive case, why isn't húfu also in the genitive?
Different prepositions trigger different cases. While án takes the genitive, með never does. When með means "wearing" or "holding", it takes the accusative case. Húfa is a feminine noun, and its accusative form is húfu.
The translation says "wearing a beanie", but doesn't með just mean "with"?
Yes, með translates directly to "with". However, Icelandic doesn't have a single everyday verb that perfectly matches the English "wearing". Instead, you use the phrase að vera með (to be with) to describe wearing clothes, accessories, or carrying items. So hann var með húfu literally means "he was with a beanie".
How would this sentence change if it meant "without the helmet" and "wearing the beanie"?