1. Yes, by construction, numerical relativity solves Einstein's equations as an initial value problem, restricting one selves to globally hyperbolic spacetimes. The <A HREF="https://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis#Weak_and_strong_cosmic_censorship_hypothesis">Strong Cosmic Censorship Hypothesis</A> asserts that all of spacetime outside black holes is globally hyperbolic.

4. For example, <A HREF="https://arxiv.org/abs/1310.7949">Template Banks for Binary black hole searches with Numerical Relativity waveforms</A>,