Learn Croatian: Njegov brat hoda kroz uski prolaz. - His brother walks through the narrow passage.

The preposition kroz (through) always takes the accusative case to show passage or movement. Because prolaz (passage) is an inanimate masculine noun, its accusative form is exactly the same as its nominative form. The adjective uski follows this same rule.

The dictionary form of the adjective 'narrow' is uzak. Why is it spelled uski here?

Two things happen here. First, uzak has a 'fleeting a'—a vowel that disappears when we add an ending like the definite -i—leaving the stem uzk-. Second, a pronunciation rule kicks in: because the voiced consonant 'z' is now right next to the voiceless 'k', the 'z' changes to its voiceless partner 's' to make the word easier to say. That gives us uski.

I've learned that the instrumental case alone can mean moving through a space. Could we drop kroz and just use the instrumental uskim prolazom?

You could, but kroz plus the accusative is a much better fit here. The instrumental of space is usually for moving around in a broad, open area, like walking through a park or a city. Using kroz emphasizes physically penetrating or passing directly from one side to the other of an enclosed space or obstacle, which fits a narrow passage perfectly.

Could I use the verb ide instead of hoda here?