I don't think you can answer these questions with theorems or experiments about models of computation (which is how TCS answers questions), so I don't think they are TCS questions.
They are, however, central questions in the philosophy of computing.
They are, however, central questions in the philosophy of computing.
Those questions may be considered philosophical now, while they are not understood, but what happens once they become understood (presuming that happens)? Say we had a precise understanding of what computation was - wouldn't that become a central theoretical part of computer science?
For example, I once worked for a distinguished engineering professor who told me about he started his career building simulation models of fluid flow using hydraulic analogue computers. Note that they constructed mathematical models of the fluid flow and then solved these using hydraulics - it wasn't an attempt to simply copy the "real" systems being modelled into an idealised experiment. In this case the fluid in the simulation was arguably "computing" in the sense you mean - but there was nothing that looked like a digital computer or a program or even an algorithm.
In this case the fluid in the simulation was arguably "computing" in the sense you mean - but there was nothing that looked like a digital computer or a program or even an algorithm.
I would suggest that you need a solid understanding of what computation is in order to properly answer the question of whether that case really is the same, in a fundamental sense, as more familiar computation, despite these (perhaps) superficial differences.
I can see at a philosophical level the question is of interest - but arguably at a practical or theoretical level the question is either irrelevant or can't really be stated.
What it a better understanding of what computation is helped you analyse what was going on in biological information processing?
The thing is, we can't predict what benefit might come from some new theoretical understanding.
Take Quantum Mechanics for an example. All sorts of practical things have come from it, but there was no way to predict what these would be before fact.
So yes, it's an interesting philosphical question - but it's meta to the level that most people are actually interested in.
[NB - I am not a physicist, so take any of my statements about what QM is or isn't with a pinch of salt!]
That's fine, and there very well may be some issues here that are worth investigating that don't just involve figuring out a definition. But your specific questions, "What makes something computation", and "What is it about a physical process that means it is performing computation?", both hinge on a blurry notion of "computation" that needs to be pinned down before they can even be taken on.
Because if we take the first definition of the word from Google, "The action of mathematical calculation", then the answer is pretty trivial: a physical process is performing a computation if the states of the physical system reliably map to the result of a known mathematical operation, no more, no less. Now, we may quibble over what is a useful computation, whether a computation is happening if we don't observe it, etc., and that's the kind of tightening of focus that's necessary to get any answers in these situations. Those tightenings are not implicit in the word "computation".
This is a typical philosophical problem - questions like "what is consciousness?" and "what about a physical process makes it conscious?" may be answered in a straightforward manner by going to the dictionary (google (Define consciousness) -> "The state of being awake and aware of one's surroundings"), but answers along those lines reliably fail to satisfy philosophers because they don't actually mean "The state of being awake and aware of one's surroundings" when they use the word "consciousness", they're using some personal tightening of the term that carries a lot of unspecified baggage (or perhaps they'll hide this baggage in "awake" or "aware", which just shifts the issue). Arguments then ensue about the right definition of the word, the one that matches the "know it when I see it" feeling that each person involved has about it, and little progress is made because nothing is pinned down concretely enough to actually discuss.
For a long time humanity has been interested in understanding what physical matter is, and progress on that has been made by understanding how the phenomena actually works, rather than by trying to define what matter is.
I would suggest that people are assuming that, since there appears to them that there is disparate computational phenomena, asking "what is computation?" must just talking about the definition of a term. But perhaps we just need to get a clearer understanding of these cases and we'll see that there is just the one kind of thing going on in all of them. I don't think anyone has any evidence to suggest it couldn't be like this.