Computations emerge from physical laws. If consciousness is "just" a complex computation, then it can emerge by the exact same process as Linux emerges from electrons and rock.
I will also note that, whatever else it means, consciousness implies some kind of identity - this human vs that human, this rock not that rock. But, this means that there can be no intrinsic physical property related to consciousness at the elementary particle level, as all electrons are perfectly identical, all protons are perfectly identical and so on. If electrons were to have some property of identity, some minimal quantum of consciousness, and so if individual electrons were different from one another, quantum mechanical statistics would look entirely differently and so the world would be entirely different.
Of course, you can still ascribe some non-physical, transcendental concept of consciousness to each electron, a soul of its own, as arbitrarily complex as you want to believe it, and there will never be any way to prove or disprove it's existence.
But the feeling of something is a different thing entirely, it is an entirely different category of thing, it isn't a number, it isn't a thing. Do what I said in the first instance, pinch yourself. Feel the sensation, appreciate that there is a thing that it is like to experience the sensation. Then try to understand how the experience can arise from the matter. When you argue this point entirely within the confines of the abstract machine of scientific reason then you lose connection with the only piece of information that you can ever be certain of: That things feel like something, qualia is real. All other things that you may think about the world are guesses.
On your second point, I believe that the physical world is entirely an expression of consciousness. So it follows that the study of physics is the study of consciousness from an external viewpoint. The action of consciousness is physics from the external viewpoint and what we feel is what physics feels like from the inside. So if quantum mechanics proves that there is no identity to this electron rather than that electron, then it follows that this electron has the same consciousness as that electron. Because fundamentally matter and consciousness are the same thing.
When you take a strong materialist line you are disagreeing with a great number of highly influential and deep thinkers with academic credentials as long as your arm. You are also arguing against one of the favoured viewpoints of contemporary philosophers.
I fully agree that there is no way to prove this position is wrong, but I think you also have to accept that you can't prove that materialism is wrong. I would say materialism is more useful than solipsism or transcendentalism, but this is a subjective assessment.
Just like a computer can sort numbers, a human brain can produce thoughts and speech, and describe itself to itself, which we call consciousness.
A machine that would both (a) have enought information about the working of the world, and (b) have the right algorithms for predicting how to influence human beings and other conscious animals would, I believe, be able to turn this same predictive ability on itself and come up with what we call "conscious experiences".
While I can't claim it's impossible that there is more to it than that (perhaps only beings imbued with transcendent souls by a god can actually have conscious experience - that is not ultimately disprovable, after all), I also don't see any reason to imagine that there MUST be something like "consciousness" that is apart from complex computation.