Since there is no horizon here, we run into no problem with having a singularity in the state at that time. Evolving the classical matter gives us a final static state which is a Schwarzschild black hole. That's right, in the out region the state looks like the Hartle Hawking state. So why do we bother with the Hartle-Hawking state at all, instead of just using the Unruh state for everything. Simply because the static state contains all the relevant features and is so much easier to work with.
Static solutions are always simpler to understand and utilise.
I don't think you can do it. In order to answer this question definitively, one would have to do the backreaction to see what is happening. This has not been done, to my knowledge. The rate at which the collapse and the evaporation happen are governed by the size of their relative stress-energies. Since the collapse is classical and the evaporation is one-loop, the relative rates are expected to proceed something like the raio of the mass of the collapsing body to the Planck mass.