supernova - Stellar mass limits for Neutron Star and Black Holes

A succinct summary of supernova types is given in the following image based on Heger et al. (2003):

^{Image courtesy of Wikipedia user Fulvio 314 under the Creative Commons Attribution-Share Alike 3.0 Unported license. The graph is based on the graph in Fig. 1 of the linked paper.}

The pair instability realm is upwards of ~100 solar masses, though it is metallicity-dependent (Question 3). As Figure 1 (below) shows, neutron stars form in the mass range of >9 solar masses - again, this is metallicity-dependent (Question 1a). Starting at around 25 solar masses, black holes will form (Question 1b).

I'm not aware of ways to form an astronomical black hole or neutron star not involving a Type I or Type II supernova without resorting to speculative possibilities like primordial black holes, but that doesn't make it entirely out of the question.