As Randy said, we can't always find solid logic between words in given language, however, according to some science sources, this may give some explanation: "Spacecraft" is just a vehicle that can travel in space, hence the name. "Cosmic rays" travel through space as well, but they're emitted by celestial objects. "Cosmic" in this case means extraterrestial, originated in outer space, coming from objects like distant stars or supernovae. Space itself (as an empty space between objects) doesn't emit any rays, that's why "space rays" isn't correct.

One might say "space rays", but likely no one would understand your meaning clearly. Please do not consider logic too much in your study of language; it often does not have any influence.

No, you can't speak of "space rays." In English, and I imagine in other languages, certain short phrases acquire meanings of their own... and certain meanings can only be expressed with SPECIFIC combinations of words. It is an extreme case of a colocation. It's a name. The name of these rays is "cosmic rays." It's just like the phrase "The United States of America." That's the name. You can't say "The Unified States of America" or "The Association of Former British Colonies of America" or "The Ex-Colonial Union of America." Certain elements neodymium and yttrium elements are called "rare earths." You can't call them "the scarce earths" or "the anomalous earths," their name is "rare earths." A certain musical style is called "Country and Western music." It isn't "Western and Country Music." A certain United States car company is "General Motors Company," not "Universal Motors Corporation" or "Durant's Automobile Company." The colon is "the large intestine," not "the big intestine" or "the great intestine" or "the grand viscera."