They burn solid fuel in a small enclosed chamber with a shaped nozzle, or two kinds of liquid fuel that are lit in a small chamber.
Engines
No. Jet engines draw oxygen from the atmosphere to mix and burn with jet fuel, and cannot function in a vacuum. Rockets carry their own oxygen, and can travel in the vacuum of space.
All rockets use the same fuel and US has used the same platform for ages. If you mean model rockets, D engines are the most powerful.
Yes ... but not with chemical engines - we need ion rockets - or perhaps nuclear engines.
Air breathers are engines that breath air as opposed to rockets which do not.
Internal Combustion Engines.
Fire needs oxygen in order to burn, and there is no oxygen in space, so rockets must take oxygen with them.
Some rockets do have wings. Then again if the rocket operates in space, wings won't do any good. Most big rockets have control systems that swivel their main engines to balance the rocket.
Rockets are steered by various means, such as tilting the main engines, moving fins, and firing reaction thrusters. This is usually done fully automatically, by computer.
No. Why would you think so?
It is hydrogen and oxygen, these two gases are mainly used in rockets
Rockets take off to carry things (called payloads) into space. Do you mean 'how' do rockets take off, or how do rockets work?