Learn Croatian: Možeš doći kad god imaš vremena. - You can come whenever you have time.

The particle god adds the meaning of "-ever" to question words. Since kad means "when", adding god makes it kad god, meaning "whenever" or "at whatever time". It shows that the exact time doesn't matter.

Is there a difference between kad god and bilo kad? Could I use bilo kad here?

They are similar, but they act differently in a sentence. Kad god acts as a conjunction connecting two clauses, like here: "whenever (you have time)". Bilo kad means "anytime" and usually stands alone. You could say Možeš doći bilo kad. (You can come anytime.), but to connect the action directly to the phrase imaš vremena, kad god is the right choice.

Why is the word for time, vremena, in the genitive case instead of the accusative vrijeme?

This is a use of the partitive genitive. In Croatian, when you are talking about an unspecified amount of an uncountable noun, like "some time", you often use the genitive case. So imaš vremena implies "you have (some) time".

Do kad and god always have to be written next to each other?