Solar system sized air sphere black hole, and some questions regarding it First of all, I'm not a physicist, I'm just a curious computer science guy, so pardon my non-technical views of this.
Now, suppose we somehow manage to fill a solar system sized spherical space with air, I know that this density would be enough to form a black hole (actually a bit of a larger sphere, but you get the idea).
I imagine one could freely move around the central area of this region for a while with no problems, given you were already there when we magically filled the space.
So, considering this scenario, I have a couple of questions:
1) Is this exactly a "common" Schwarzschild black hole for a distant observer?
2) Is it correct to say that at this moment the singularity of this BH lies in the future for every possible observer, since the mass has yet to collapse?
3) How long approximately would it take, in proper time of the air particles, for them all to collapse together at the singularity?
4) Now, if this mass of air were rotating infinitely close to the speed of light, would that increase this time to the same as how long it would take for this BH to evaporate for an external observer, since the air particles would be orbiting the center of the structure and falling ever so slightly?
EDIT: After a bit more thinking, I think the proper time would be exactly the same, since time for these particles would now be extremely sped up as a consequence of them moving close to the speed of light. Is this correct?
5) Did I just define a Kerr black hole in (4)?
 A: The problem with your scenario is that you're ignoring mass and gravity.
Earth's atmosphere weighs about 5.1 billion billion kg.  Spread around the Earth, held by the Earth's gravity, a column of air weighs above you weights about 14.4 lbs per square inch.
To fill the solar-system with air, equal density, to about 30 AU, you'd need (not going to calculate), millions of solar masses of air.   Gonzo/nutso amounts of mass, millions of times the mass of the entire solar system.  Trillions of times the mass of Earth, ten or 100 quadrillion times the mass of Earth's atmosphere.   That's a lot of mass.
If you were inside that much mass of air, it wouldn't be like floating/flying around, that much air would crush you, flatter than a pancake, in a microsecond.   Flat enough to undergo fission.  Rapid fission in fact.   You can't have millions of solar masses of anything in a region the size of the solar-system without gonzo-nutso-super gravity.
It's a nice idea that it would just be air inside, but it wouldn't be like that.  You'd have collapsing very dense mass that would rapidly approach a singularity at the center, and empty space, but the empty space would be inside the event horizon so there's be no escape and only one destination - the singularity.
1) is this common - no.  Black holes are made from collapsing giant stars or collapsing Neutron stars.  They aren't made by vast amounts of gas in regions the size of the solar-system.  (Perhaps the very early supermassive black holes were - their origin isn't 100% understood.
2) The inside of a black hole can be observed, so I'm not sure what you mean by lies in the future for every observer.   Everything inside the black hole has a future date with the singularity, but they cant see the singularity, they're just flying towards it.   Light doesn't travel from the singularity to those falling into it, so it can't be seen.
3) nothing will travel faster than the speed of light, so for a solar-system sized collection of mass, you can calculate a minimum time, but for the actual time . . . somebody smarter than me should answer.   Also, time from who's perspective?
4) Rotation inside the black hole . . . I don't think that would avoid anything, but I'm not sure what to say about how much time.   Orbits inside the black hole are tricky.  They might or might not be possible.
5) a Kerr black hole is a rotating black hole so in a sense, your question #4 might apply to #5.   A Kerr is more of a mathematical solution.   I'm not sure they're real.
