Dear Constantin
You write:
---"At the center of a black hole the spacetime curvature becomes infinite: the time has stopped, and gravitational length contraction tends to infinity."---
Though the value of a quantity may not have a limit, in practice the properties of any physical object can be expressed in finite numbers. That we cannot measure or calculate them doesn't mean that the quantities are indefinite. So the curvature does not become infinite, but just extremely great. Similarly, time does not stand still, it just proceeds at an extremely slow pace, and lengths do not become zero, but are contracted extremely. Another point is that as any measured or calculated quantity of some object depends on the distance it is observed from and the field at the observer, then we must add to any value we find, add the specifics of the observer-observed relation. Since to someone nearer the hole, where its field is stronger, time inside the hole proceeds at a faster pace, then the hole to that observer is a different object. We cannot, then, speak about 'the' hole, as if it has some absolute properties of itself, independent from any interaction the hole may be involved in. If we nevertheless do, then we declare our observation position in space as well as in time to be more unique than any other point, which is not what Galilei would approve of.
---"Hence, 'sitting' inside a black hole you'll say that the Universe doesn't exist, has no physical reality."---
Indeed: as seen from deep inside the hole's field, we, our world doesn't exist, not yet or no more or never will exist, so what happens here has no effect on the hole nor on the hypothetical observer inside of it, any physical interaction too far redshifted to be of any consequence.
---"even if you do not see the Universe, it does not mean that the Universe doesn't exist, has no physical reality'."---
To say that an object exists whereas we cannot in any way by observing or interacting with it check whether it exists or not requires supernatural abilities. In nature objects only have reality, exist to one another as far as they interact. Similarly, if your friend sits a hundred meters from you on the beach, then the effects of him disturbing the sea by dipping his finger in it on the waves where you sit are nil. His action cannot be retrieved, be reduced from the wave pattern you see, so his action has no physical reality to you. As far as you are concerned, it has not happened, even if your friend calls on god as his witness that he really did dip his finger in the water. I'm afraid that in our mind we're so used to the company of such a silent witness who's always looking over our shoulder that we assume that the things we see have an absolute, autonomous existence, independent of whether we observe it or not, independent from any interaction. As a result we assume that things which cannot be observed nevertheless can exist. They sure may exist elsewhere/when, but then they exist to another observer. The point is that by thinking about the universe as a whole, we ascribe it properties and thereby assert that there's something outside of it to which it matters what its properties are, as if it is embedded in something which interacts with the universe. By doing so, we actually declare that the universe has been created by some outside intervention, an act of belief which makes the properties of everything inside of it incomprehensible. In a universe which creates itself without any outside interference, particles have to create one another, so they are as much the source as the product of their interactions and exist only within this relation. The consequence is that we cannot speak about their properties as something which is independent from anything, as if it is an absolute, objective, intrinsic, 'hallowed' feature of particles.
---"And here you are wrong about that perfect isolated systems 'cannot show any behavior. If we could isolate it, we'd annihilate it.'"---
What I mean is that if particles only exist to each other as far as they exchange energy or interact (unlike a net energy transmission associated with interactions, their energy exchange is unobservable), then they would stop to exist to each other if by isolating them from each other, we could cut off this exchange. In practice, however, we can only isolate particles to prevent them from absorbing energy in certain frequencies. If we cool a cloud of identical particles to their ground energy and suck most of their kinetic energy away from the system, then their mutual energy exchange becomes so orderly, so strictly coordinated that the cloud starts to act like a single object (BE condensation). It is this continuous energy exchange between particles which is at the heart of quantum mechanics. Though we may impede particles to absorb energy from the outside, that doesn't mean that their exchange with the outside world is completely cut off -in which case they wouldn't feel any gravity from the Earth. Besides, we can only observe their behavior in containers cooled to 0 K if they are not isolated from our observation interaction.
Regards, Anton