this guy is one of those "modern science is wrong because i don't understand it" types. and this is the first time i can't see a flaw in his logic. what am i missing?

The basic flaw is that there is no satisfactory theory describing "before" the big bang. Since it did happen his idea has been refuted by experiment. For all we know the entire universe is a big black hole. There is no good theory of what goes on inside a black hole either.

Another point is that the equations of general relativity are time-symmetric, meaning that if you take any time-evolution allowed by the laws of physics and play it backwards, this time-evolution must also be allowed by the laws of physics. So density alone cannot automatically lead to collapse--that's why, in addition to black holes, general relativity also allows for "white holes" which are perfect backwards mirrors of black holes, they constantly spew matter outward from a central singularity instead of pulling it in, until the singularity disappears. White holes are thought to be ridiculously unlikely on thermodynamic grounds (after all, the equations of physics governing a falling egg are also time-symmetric, but we're very unlikely to see pieces of broken eggshell spontaneously reassemble themselves into an intact egg), and the big bang is not thought to be a white hole, but I think you can sort of make the analogy that white holes are to black holes like the big bang is to the big crunch.

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?

2. Even if GR were to apply under these conditions, wouldn't time practically grind to a halt under so much gravity (as GR would predict)? Let's say a particle has probability p(t) of escaping from a black hole at or before time t. With time stopped, the matter inside the black hole would have "an eternity" to escape from it. Given "sufficient time," a lot of matter could have had a chance to escape, even for small p. (One may be able to derive a formal hazard function.) I am not saying the universe was born like this; but even if one were to start from the premise of the question and think it through, one may come up with various answers, none of which is a priori worse than all matter being stuck in a black hole with no chance of escape whatever. (Added later: As far as I remember, S. Hawking lost a bet with another famous physicist when observations showed that particles can and do escape from a black hole ordinarily.)

So according to this, "gravity" and "expansion" are simultaneously determined; it's not okay to assume a value for one and then solve for the other. (E.g. you may not assume expansion = 0 and solve for gravity [itex]\longrightarrow +\infty[/itex].) 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?

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...).

sthepeh hawking has explained this thin. as we see a black hole every moment it is losing energy by the laws of thermodynamics. at last point when it looses its all energy/mass it is destoned to explode. the big bang matter exploded as it had no other choice.