1. You assume correct that I define a black hole as a volume of high density mass. This holds for any black holes that we might find orbiting in a binary star system, or at the center of a galaxy. The Schwarzschild equation for the radius of the black hole suggests that as a black hole gets more massive its average density will decrease. Extrapolating this idea, a black hole as massive as our universe might contain matter so sparse that one wouldn't hit anything upon falling into it. One would just keep coasting through near-vacuum. So, it is possible for a black hole to be a volume of low density mass, but only if the total mass of the black hole is extremely large.

2. I suggest the universe has a finite mass. Therefore, by virtue of their mutual gravitational attraction all particles of matter will stay within the event horizon of the universe, which is just an imaginary boundary beyond which nothing can escape. Since there is no matter or energy outside the event horizon, there is nothing outside the event horizon. Space implies relative positions (distance) between clumps of matter. Since there is no matter outside the event horizon, there is no means of measuring distance or velocity. One cannot even say that it is empty space outside, since it is not possible to make that assessment.