1. Commonly, Corners and Monte Carlo are the different  types of simulation. You can do Monte in different corners separately. However, as a rule, Monte is done only in the typical  corner.
2. Number of run it is just the matter of accuracy. With 100 runs you accuracy is about 1%.
3.
a. As a rule, Vth mismatches decrease with 1/sqrt(W x L)
b. For the MOS transistors, mismatches are worse in a weak inversion  
c. The stress sensitivity of Vbe or Vgs voltages is proportional to their charge carrier mobility, making PMOS or PNP transistors with symmetric topology pproximately 3 times less sensitive to the mechanical stress then NMOS or NPN ones.