Learn Croatian: Bez državljanstva ne možeš glasati. - Without citizenship you cannot vote.

The preposition bez (without) always requires the noun following it to take the Genitive case. Because državljanstvo (citizenship) is a neuter noun, its Genitive singular ending is -a.

Why is "cannot" written as two separate words (ne možeš) when things like "I don't have" are written as one (nemam)?

In Croatian, the negative particle ne is almost always written separately from the verb, just as it is here. There are only a few specific verbs that merge with the negative particle: neću (I will not), nemam (I don't have), nisam (I am not), and nemoj (don't).

I've also seen the word glasovati used for "to vote". What is the difference between glasati and glasovati?

They mean the exact same thing. Glasovati is often preferred in formal, legal, or political contexts in Croatia, but glasati is much more common in everyday casual speech. You will see and hear both, so you can use whichever you prefer.

Does ne možeš refer to "you" specifically, or is it a general statement?

It can be either, depending on the conversation! Just like in English, Croatian often uses the second-person singular ("you") to express a general rule or fact that applies to anyone, which translates smoothly to "one cannot vote".