I believe Roy told Hikaru maybe in the first episode that they had thermonuclear reactors for powerplants. So they technically don't run on any fluid for fuel which was the big limitation of the VF-0 since it ate up gas so quickly and they always had to retreat.
And as for could they fly in space, if you give anything enough thrust to overcome its own mass since there no drag, it will move. You could stick a rocket on a cube shaped ship and it will still fly. The only reason our space shuttles are shaped like aeroplanes is that they have to fly in and out of the atmosphere. This is one of the big reasons they are building the space station so that they can build atmosphere-free ships.