My summary I guess:
Diameter (or Radius, as you have used) is related to the density and the mass, so that rules it out of the options.
Temperature is completely irrelevant when creating a planet, as temperature changes depending on distance to stars, etc.
Type of object is not really important, because when creating a galaxy, you cant use materials. Unless, of course, you try to change the composition of the black hole in the center (if there is one in the galaxy in question-- Yes, some smaller irregular galaxies do not have a large heavy hump in the center like a black hole). The only difference between asteroid, planet, etc is mass. So that kind of rules that out.
Materials also affect density, so that rules density out, which rules radius out, as density affects radius (going in a loop to where I started I guess)
Creating a galaxy seems a bit difficult, creating a center black hole isn't so hard, but there will have to be some sort of procedural cluster generator for the galaxy star particles, unless you can create a template for the generator (ie. Seed)
Radiation is irrelevant in creating a planet, as radiation is simply another form of photons. (photons collectively are radiation, eg. Infra red radiation is lower energy photon radiation ie. Heat, which rules radiation out as it simply mimics temperature in this case)
Additionally, the difference between a planet and moon is not in the physical object itself, but what it is orbiting. So it is probably a good idea to merge them into planet/moon.
In general, these fallbacks seem to make the whole thing a bit trippy. For now, it is much easier to spawn in a planet and edit it's parameters. You can even pause time while editing planets so that their changes in gravitational pull don't affect objects so much.