No, there is no reason to think that the human brain is capable of computing anything that isn't Church-Turing computable. Luckily no translation actually requires a "general solution" of the problem formally.
Sorry, missed this. I'll try to explain. A real computer doesn't actually have an infinite tape (memory) like a canonical Turing Machine, it's actually a finite state machine with a vast amount of possible states that we conveniently think about as analogous to a Turing machine, hence the the halting problem is actually solvable (just not in practice) for real hardware.
Given content that can be expressed in two languages in a text of finite length, you could in theory enumerate all the possible translated texts.
Maybe there are examples of texts that can't be translated even by humans? Language Log has discussions about so-called words that can't be translated regularly and generally rejects that concept, but maybe whole texts are more difficult. The I-Ching has several translations that don't resemble each other very much and it's common knowledge that a translation can be either accurate or beautiful but rarely both.
It is hard to say what the non-physical is. However, it can be detected. For example, if we could, say, solve the halting problem, then whatever part of us is doing the solving cannot be physical, since everything physical can be computed by a Turing machine.
So, in general the non-physical is defined negatively. The physical is defined by physical limitations, i.e. the laws of physics and computation, and thus anything that surpasses those limitations is non-physical.
There is no algorithm for checking whether a system can solve the halting problem or not, the reduction to the halting problem is quite simple. But that's besides the point.
If you found something that could solve the halting problem and you're lucky enough to be able to prove it for this special case, that would just mean that the assumption that everything physical can be computed by a Turing machine is wrong. It works the same way with anything else that we think of as "impossible". If you observed an apple falling towards the sky that doesn't mean that the apple is non-physical, it just points to a serious flaw in our understanding of gravity. Experiments trump all physical theories.
Technically, we already recognize the world is non-physical. Materialists defined materialism to things bumping into each other. Now we know there are things like field effects, attraction, and action at a distance. So there is a non-bumping substrate that the bumping things exist within. Thus, strict physicalism is already known to be false.
No it doesn't. It just implies that everything that causally interacts with the observable reality is physical. It leaves open the door for an immortal soul, it's just that the existence or nonexistence of the soul has absolutely no effect on the observable universe.
The term physicalism was introduced a few decades after we figured out Maxwell's equations. If the philosophers defined it to mean things bumping into other things they were frankly poorly informed about the world we live in.
When we will have created human-level AI, changes in language translation will likely be a minor detail on the background of other changes in the world.
Your question sounds like you assume we have a perfect understanding of the brain. At best, our understanding is still very much peripheral. We have no idea how consciousness forms, even if we roughly know where it is located.
No, I didn’t assume we have a perfect understanding of the human brain, simply that nothing magical is happening and that we will eventually be able to better understand it.