1. In the beginning, was there light? If there wasn't light, would GR apply? If it wouldn't, can one really use one of GR's predictions and say infinite mass would result in a black hole?
Einstein's theories of relativity are about the universe itself, not the things in it. There exists a maximum velocity, and light happens to travel at that velocity (because it has no mass). So light has absolutely no relevance to the applicability of GR.
" But it is possible to come up with a system of equations that simultaneously determine gravity and expansion shortly after the Bang. (Sort of like, xy = -1 and x + y = 0?) Is this an accurate representation at some level?"
Yes, Einstein's Field Equations of GR are a system of equations that simultaneously determine gravity and expansion (gravity and expansion are united as part of "the curvature of spacetime"), given the distribution of matter.
But the distribution of matter is governed by the Navier-stokes equations of fluid flow, so these must be combined with GR to form a system with a unique solution.
Unfortunately, EFE and NS are a system of nonlinear partial differential equations in 16 unknowns, involving thousands of individual terms, rather then being a system of linear algebraic equations.
So yes, on some level your representation is spot on accurate (in analogy your constants -1 and 0 are like the initial mass and curvature condtions...).