Learn Croatian: Junak luta mračnom šumom. - The hero is wandering through the dark forest.

This is the bare instrumental of path (also called the prosecutive). With verbs of motion like luta (is wandering), the instrumental case on its own shows the space or route through or along which the movement happens.

Could I use the preposition kroz (through) here, like kroz mračnu šumu?

Yes, but there is a slight difference in feel. Using kroz with the accusative emphasizes a clear trajectory from one side of the forest to the other. The bare instrumental (mračnom šumom) focuses on the space itself, suggesting the hero is wandering around within the forest, which perfectly matches the verb luta.

Both the adjective mračnom and the noun šumom end in -om. Is this standard for the feminine instrumental?

Yes! For feminine nouns ending in -a (like šuma), the instrumental singular ending is -om. The matching adjective also takes the -om ending (from mračna to mračnom), making it one of the friendlier noun-adjective matches to remember.

What kind of motion verbs typically take this bare instrumental of path?

You will mostly see this with verbs describing continuous or aimless movement, such as lutati (to wander), šetati (to walk or stroll), hodati (to walk), or putovati (to travel).

Is there a difference between and for the word hero?