I am going to take a very different view on what computer science is, concluding that math is a subset of CS, not the other way around.
Math, CS and all the other "numerical" and "information" sciences are giving us a view into a Universe that is just as real as the physical universe, but because it is an Information Universe, we can only describe and experience it with these sciences.
For example, it almost certain now that we are not going to make a computer or another device that can view into this Universe, not unless it is equivalent to a Turning Machine in terms of its computational capabilities.
We can describe all kinds of theoretical castles in the sky about this universe (pure math and theoretical CS for example).
But, if we really want to look into this Universe, experiencing it first hand, we need to build physical computers and data networks, which are to the information universe as spaceships are to the physical universe. Plus, we need systems to power them (software) and development concepts about how to live in that Universe (software engineering and IT).
So, math/theoretical CS shows us where the door is, but we cannot walk through that door without the practical tools: the machines and vehicles we need to move around in the information universe.
Like all Universes, it has "physical laws," like the Halting Problem, Rice's Theorem, etc. It has implications of those laws (my three laws of software engineering, Brooke's law, algorithms must be finite in time and resources, etc.).
It has stuff we know for sure (how to construct CPUs to allow us to manipulate the universe, that all our tools/machines/etc. must be finite, etc) and so forth. There are already life forms (algorithms and theorems) and a macro structure (data structures and abstract geometric concepts).
We have not met any advanced life forms yet (AI). There are things we think must be true, but we can't yet prove/disprove (P!=NP, the Church-Turning Thesis, etc.). There are illusions of reality (Silicon Valley, etc.).
The list could go on and on..............
But, it is a real Universe that we have only been in--in any meaningful way--from the time of the telegraph and Ada's conceptual leap, when she realized that computations were fundamentally symbolic and symbols interchangeable.
So, no wonder we are still infants, learning how to keep eye contact.
However, it is incorrect to say that the Information Universe is any more or less plastic than the "physical" universe, so your assumption on point #1 is just wrong. As there are laws of the "physical" universe, there are laws of the Information Universe.