Why are space suits of fire fighter suits covered with a shiny metallic surface?
The "space suit" firefighting suit is shiny and metallic on purpose.
Why is it metallic? The "Space suit" is supposed to be fireproof. Most conventional firefighting suits are made of rubber or plastic. While rubber is naturally fire resistant, it will burn if it gets hot enough. Ditto for most plastics. Metals will also burn if they get hot enough, but the ignition temperature for most metals is much higher than for rubber or plastic. This is heightened by the fact that the primary metal used in these suits is gold. Gold is used because it's shiny (more on that later), it can be pressed into very thin sheets which keeps the suits from becoming too heavy, and it is a "noble" metal. Like Noble gases, noble metals don't readily form compounds with other elements, and that makes them even more resistant to ignition (an oxidation reaction) than other metals.
Why is it shiny? Shiny materials are perceived that way because they reflect light energy. We see the visible spectrum energy in the form of "shine" or "reflections." However, these materials reflect more than visible light, they frequently reflect ultra-violet and heat. Heat is the important energy. By reflecting heat, "space suit" firefighting suits can allow firefighters to get much closer to more intense fires than firefighters in conventional equipment.