Learn Croatian: Iznenađen sam koliko je grad lijep. - I am surprised how beautiful the city is.

In English, we use 'how' to express the degree of an adjective, like 'how beautiful' or 'how big'. In Croatian, you must use koliko (how much) when talking about the degree or extent of an adjective. Using kako would incorrectly sound like you are talking about the manner in which the city is beautiful.

Why aren't koliko and lijep right next to each other, like 'how beautiful' is in English?

Croatian word order rules split them up. The word koliko starts the second part of the sentence. Because the verb je is an enclitic (a short grammatical word without its own stress), it demands the strict second position right after koliko. That means the adjective lijep gets pushed to the end, giving the literal word order 'how much is city beautiful'.

If a female speaker is saying this, does the sentence change?

Yes. The word iznenađen (surprised) acts as an adjective describing the speaker, so it must agree with their gender. Because it ends in a consonant here, we know a man is speaking. A woman would add an -a to the end and say Iznenađena sam.

What case is grad in here?

It is in the nominative case, which is the standard dictionary form of the word. It is the subject of the second half of the sentence ('the city is beautiful'). The adjective lijep also takes the masculine singular nominative form to match it.