Learn Polish: Nie mamy benzyny. - We have no petrol.

Because the sentence is negative. Normally, the object you have takes the Accusative case (like Mamy benzynę). But in Polish, when you make a verb negative (nie mamy), the direct object must change to the Genitive case, which is benzyny.

Why isn't there a word for "we" in the Polish sentence?

In Polish, the verb ending usually tells you who is doing the action. The -my ending on mamy already means "we have". You only need to add the pronoun my to say My nie mamy benzyny if you want to emphasize it, like "WE don't have petrol, but maybe they do."

How does Polish handle the English phrasing "have no"?

Polish doesn't use a word for "no" attached to the noun like English does in "have no petrol". Instead, you simply make the verb negative. You put nie directly in front of the verb to get nie mamy (we don't have).

Can I use benzyna for any type of car fuel?

No, benzyna specifically means petrol or gasoline. If you drive a diesel vehicle, the word you need is ropa (which literally means "oil") or olej napędowy.