"On n'a plus d'essence."
Translation:We're out of gasoline.
"Essence" = petrol (UK), gasoline (US), but also shortened to "gas" (US). "Fuel" is also accepted here. Depending on what you mean, "gas" may refer to "l'essence" (gasoline-US) or natural gas (gaz). In regard to "North Americanism", you make it sound like a bad thing. It is commonly used in the States just like "petrol" is used in the UK.
Yes, but often in oral French the "ne" is dropped. So even for negative sentences it may be said (but not written) "on a plus de..." meaning "we have no more."
However, it is still possible to distinguish between a spoken negative sentence and a positive one. In a negation, the "s" at the end of plus is not pronounced. In a positive statement the "s" is pronounced.
Here's a very helpful video about "plus."