A "blade" is a more vague term for something that is sharp or thin, and isn't usually said on it's own (blade of grass, knife blade, razor blade, ice skate blades) You can shorten to just "razor," but this typically what native speakers will think you're talking about ( http://freesamples2fillupyourmailbox.com/wp-content/uploads/2013/09/Gillette-Venus-Embrace-Razor.jpg ). American english is full of words that are unnecessarily specific (eyeglasses vs. glasses, horseback riding vs. horse riding)

I would say that the blades are part of the razor. For example, a Mach 3 is a razor with three blades. A Schick/Wilkinson Quattro is a razor with four blades.

English uses "razor blade" for the same reason Chinese uses 剃刀 and not just 剃 or 刀.

"Razor" usually refers to both the handle and the blades, but "razor blades" refers specifically to the blades. Example: I need new razor blades for my razor. You could also say "I need new blades for my razor," because it would be clear from context that you mean razor blades and not some other kind of blades (like knife blades).