Learn Croatian: Jesi li svjestan na kolikoj brani stojimo? - Are you aware of how large a dam we are standing on?

The preposition na (on) requires the locative case when indicating a static position or location. Since the speakers are standing on the dam, both the feminine noun brani (dam) and the exclamatory adjective modifying it, kolikoj (how large a), must take the locative singular endings.

Could I use kakvoj instead of kolikoj in this sentence?

You could, but it changes the meaning. Kolikoj specifically emphasizes the size, scale, or quantity (how large a dam), whereas kakvoj asks about the quality or type (what kind of dam). Using koliki here expresses awe at the sheer magnitude of the structure.

The adjective svjestan (aware) is masculine here. How would this change if I were asking a woman?

You would use the feminine form svjesna, making the phrase Jesi li svjesna. Notice that the 'a' in svjestan is a 'fleeting a' which disappears when you add the feminine ending, and the 't' also drops out to make the resulting consonant cluster easier to pronounce.

Why does the preposition na come before kolikoj brani instead of at the end of the sentence like in the English translation?

Unlike English, Croatian grammar strictly forbids ending a clause or sentence with a preposition. A preposition must always sit immediately before the noun phrase it governs. Therefore, na has to precede kolikoj brani, resulting in a literal structure of 'on how large a dam we are standing'.