Please excuse my lack of jargon know-how, but the stuff coming out of the bottom of rocket ships looks very hot! Why doesn't this melt or burn the structures erected around it?

Whenever you see the Starship Enterprise off on a mission, an 'outside' shot always shows the vessel in full visiblity - but how visible would it be? must you always be illuminated by lights on the top, or a planet nearby? If we were away from any planets and suns, and I were to space walk a few hundred yards away from the ship, and it had no lights on the outside, would I only see stars and a black 'shadow' where the ship was? Or is there always residual light? could I for example see my own hand in front of my face? or is there a point where you can see nothing nearby, but only stars and galaxies in the distance?