If having two dimensions, height and width, means that a diagonal line is just a tiny line up connected to a tiny line across, repeated on a level so small we don't notice and the line appears diagonal, does that mean that everything in our 3D world is almost 'pixelated' at a really microscopic level? Sorry, I'm having problems describing what I mean but see if you can make any sense of that. =) Thanks.

There may be a debate over whether spacetime is continuous or granular: I will have to leave that to others. But there seems to be a problem with saying that a diagonal line is a microscopic staircase. If it was, then the diagonal of a one inch square would be two inches long, when in fact its length is the square root of two.

Is it possible to determine whether the laws of Physics as they are currently perceived will last indefinitely? Is there anything to prevent the nature of the universe changing so much tomorrow that reality as we know it breaks down?

This question is at the heart of David Hume's great sceptical problem of induction. He argues that there is no possible reason for saying that the laws of physics won't change overnight, since to say this would be to make a prediction, and our method of prediction just presupposes that this won't happen. Put another way, it looks like you can't have evidence that the future will be like the past, because all your evidence is in the past, so to use that to show something about the future would require that you already know whether the future will be like the past. There has been a great deal of productive work on the problem of induction, but nobody has come close to a full solution. If you want to get into this great issue, the best place to start is Hume's classic discussion in his Enquiry Concerning Human Understanding , especially sections IV and V.

I believe that it is assumed that the 'laws of physics', as we know them, apply throughout the universe. Is this a reasonable assumption or is our concept of cosmic reality an error?

I agree with Alex that our best hypotheses may well not capture the actual laws of nature, and that physicists strive for unification, and I think there is a third aspect to this question. In spite of what the 20th century philosopher of science Karl Popper maintained, science depends on induction, on making inferences about the unobserved on the basis of the observed. And as the great eighteenth century philosopher David Hume observed, this depends on some kind of assumption of the uniformity of nature. Hume notoriously argued that we can have no good reason for this assumption, and that is very close to the point that we have no good reason for assuming that the laws of physics are the same in those parts of the universe we have observed as they are in those parts we have not observed. But without making something like that assumption, science would be impossible. To put it differently, to leave open the possibility that laws might be different elsewhere is, if taken to an extreme, not just to...