Question

There was no oxygen in space so how can a rockets fuel burn and accelerate the rocket

Answer 1

You only need two components for a combustion reaction: the fuel and the oxidizer. Most space rockets carry their own fuel and oxidizer with them into space, so they don’t rely on the availability of oxygen out there. Furthermore, you don’t necessarily need fire to provide thrust to a rocket; you can obtain thrust by simply ejecting ‘mass’ out of the rocket.