I may have to answer this in parts, a bit at a time, so I apologize if I'm not able to answer everything at the moment.
If I wanted to find out how to estimate, say, a planets surface temperature based on a stars temperature and distance, what is the best way to do this?
Ah, I just studied this about a week ago! What you're looking for is the effective temperature of the planet, which can be calculated as
$$T=\left(\frac{L(1-A)}{16 \pi \sigma D^2} \right)^{\frac{1}{4}}$$
where $L$ is the star's luminosity, $A$ is the planet's albedo, $\sigma$ is the Stefan-Boltzmann constant, and $D$ is the distance from the star.
how does the mass of a star relate to the distance of the frost line, and is there an already existing equation to estimate this?
I wasn't able to find an explicit equation for this, but it's calculable. The frost line is a certain distance from a star in a stellar nebula such that the temperature is about 150 Kelvin.
If you know the mass of the star, you can use the mass-luminosity relation:
$$\left(\frac{L}{L_{\odot}} \right)=\left(\frac{M}{M_{\odot}} \right)^a$$
Re-arrange that to solve for the luminosity. The inverse-square law says that the intensity of power drops off as the distance from the source increases:
$$I=\frac{P}{4 \pi r^2}$$
You can solve for $r$ if you can figure out the required intensity:
$$r=\frac{1}{2}\sqrt{\frac{P}{\pi I}}$$
Here, $P \approx L$. Figure out the necessary intensity to heat the nebula to 150 K and you've found the frost line.
To find the most likely average mass of a potential planet, what information would I need?
I can't help you much there, but I can give you a starter. The density $\rho$ of a circumstellar disk at a distance $r$ (as given by Michael Woolfson in On the Origin of Planets) is
$$\rho (r)=C \exp \left[-\frac{(r-r_{\text{peak}})^2}{2 \sigma ^2} \right]$$
where $\sigma$ is one standard deviation and $r_{\text{peak}}$ is the peak density, and $C$ is a constant.
As promised, here are some more, set forth by Woolfson.
The disk decays over time; its density at time $t$ is approximated by
$$\rho_t=\rho e^{- \gamma t}$$
where $\gamma$ is a decay constant. If you've taken certain math course, you've probably seen this equation many times before, just in with $\rho=y$ and $\gamma=k$.
Another equation - really, a couple equations - deal with accretion by a small dust particle in a circumstellar disk. The variables involved are: $m$ (mass of the particle), $t$ (time), $s$ (the radius of the particle), $\rho_s$ (the density of the particle), $\rho$ (the density of the disk), $f$ (the fraction of the medium that is dust), $T$ (the temperature), and $k$ (Boltzmann's constant, not be confused with the Stefan-Boltzmann constant).
The relevant pair of equations are:
$$\frac{dm}{dt}=4 \pi s^2 \rho_s \frac{ds}{dt}$$
$$\frac{ds}{dt}=\frac{3f \rho}{4} \left( \frac{kT}{4 \pi \rho_s^3} \right)^{1/2}s^{-3/2}$$
Using these, you can find the size and mass of a given dust particle at any given time.
