Estimation of average rock and asteroid mass associated with different stars There is a lot of information on different star types and compositions. 

Can we make estimates of the total mass of rock, ice, and non stellar matter that orbits stars based on star evolution models?

Take, for example, the sun - are there studies of the total mass of non-solar material associated with the sun and it's composition regardless of accretion. What about nearby stars?

Can we estimate how much non-incandescent material the galaxy contains aside from dark matter?
The composition of the gas from which stars and their planetary systems form is reasonably well known. About 1-2% of this gas is in the form of chemical elements heavier than Helium (the so-called metallicity of the gas).

A fraction of these "metals" - the iron, silicon, oxygen etc. is capable of forming dust and then accumulating to form "rocky" material.

So to answer your last question first, given the available reservoir it seems most unlikely that even 1% of the baryonic (normal) matter in the universe could be rocks, even if none of it were gathered into luminous stars and galaxies.

Forming stars are surrounded by circumstellar material from which planets and other rocks form. Observations of young stars suggest these discs can be as massive as 10% of the stellar mass, but more usually 1% or less. This means that as a fraction of the whole formed star system the rocks will be at most 1% of 10% (ie 0.1%) of the stellar mass. For a Sun-like star that means there's less than 330 Earth masses of rocky material around it.