1.  The CM UGBW should be comparable to the differential signal path.  Otherwise power supply noise could be amplified to the output.  Most of the time, though, you don't have a lot of choice since it can be difficult to set the CM UGBW independently of the differential UGBW.

2.  The boosting amp should be at least 3τ faster.  With a single pole model for the boosting amp, you introduce a pole-zero doublet near the boosting amp's UGBW, which can create problems with the main amp's phase margin.

3.  They all behave fairly similarly in terms of stability.  The active device architectures can greatly limit your output swing, so that turns out to be one of the major factors in deciding the architecture.