Technically, Spock's death occurred as a result of radiation exposure when he went into the reactor area and fixed the problem they were having going to warp just in the nick of time so they didn't all end up being used as building material for Genesis' new matrix, but I know what you meant.
And, yeah, that whole "Search for Spock" pretext was pretty weak. The only thing that made any sense whatsoever, (in a sci fi stetchy sorta way), was that, once on the planet, (and I believe the movie shows the torpedo being launched towards the new planet), the Genesis effect brought him back.
But a new world from a nebula? Well, ok, if there was enough matter in the nebula, I suppose your could build yourself a planet.
The whole idea of the Genesis Device was to find a lifeless world in a star system, presumably the correct distance from the star to provide earth like heat and light, then touch off the device and it would used materials from the world to create life, and "voila!" Pretty sure the planet was even supposed to already have its own atmosphere already in place, though they may not have come out and said it. But, all of a sudden, the device was capable of not only creating an atmosphere, but the planet itself!
But when they were fighting Khan and company in "Wrath of Khan," they weren't in a solar system, they were warping through space and ended up in a nebula. So, where's the sun around which this new planet revolves, or, without a sun, where did all the light come from and the heat, so as to keep all this new evolving life, including Spock, the Klingon landing party, Kirk's landing party, etc, from freezing to death?
No explanations that I could remember, just a "brave new world," presumably miraculously having found a star, "established standard orbit" around it at just the right distance to keep things alive and well.
Heck, at least they could've shown the new planet right after it was formed and they had shot spock onto it going to warp in the direction a nearby star system - and mentioned it as an "undocumented feature" of the Genesis Effect!!!