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).



It is thought to be possible for a black hole to form without a supernova (see the section of the graph marked "direct black hole"). This has not been confirmed observationally, although there are some possibilities. I've written about this in more detail here.