Composition of E. coli (dry weight): 55% protein, 20% RNA, 10% lipid, 15% other
Protein concentration is about 100 mg/ml or 3 mM. From the size of an E. coli cell, 1 nM is about 1 molecule/cell. This is ~1000 molecules/cell for HeLa cells.
Diffusion coefficient for an "average" protein: D ~ 5-15 microns^2/s, or ~10 ms to traverse an E. coli. For reference, a small metabolite in water diffuses about 30-100x faster.
Reference: Cell 141:1262, Key Numbers in Biology
This question has no particular answer. There are several families of DNA binding proteins, some of them bind specifically (e.g. restriction enzymes like EcoRI which binds to and cuts GAATTC or transcription factors like lac repressor which binds a particular point of the e coli genome about 25 base pairs long) and some of them bind semi-specifically (e.g. zinc fingers which bind GC rich regions), others non specifically (e.g. the sliding DNA clamp).
For all of these proteins, they will have a tendency to have positively charged amino acids facing the DNA because the DNA's phosphate backbone is negatively charged. There are lots of protein motifs (like the helix turn helix motif) that fits into the major or minor groove of the DNA. The lysine and argenine are important because they are the positively charged amino acids. Histidine is also positively charged, but it is not as long and flexible, and doesn't seem to fit as often or as well.
The ribosome moves relative to the mRNA by, in effect, pulling itself along it. If both the ribosome and the mRNA are freely floating and not attached to anything else (as in jp89's answer), the relative amount of movement should depend on their relative masses.
(Actually, it also depends on how much drag each of them experiences with respect to the surrounding liquid medium, but since I have no idea how much that is, and since it's probably highly conformation-dependent anyway, I'm going to just ignore that and just assume that the drag is also more or less proportional to mass, at least to first order.)
As it happens, a quick Google search and some back of the envelope calculation suggests that the mass of a ribosome and the average mass of an mRNA are both around a megadalton. Of course, the length (and thus the mass) of an mRNA varies quite a lot, so it would seem likely that sometimes it's the ribosome that moves mostly, sometimes it's the mRNA, and sometimes it's both.
Also, as shigeta and others have pointed out, there can be more than one ribosome attached to the same mRNA strand. That's going to make the mRNA move more (and, correspondingly, the ribosomes move less), since there are more ribosomes pulling it along.
Then there's also the protein being transcribed, which is attached to the ribosome but also being moved with respect to it. And I really have no idea how negligible the interactions with the tRNAs and so on are. It's a mess, but my guess would be that, usually, it's mostly the mRNA that moves, but that the ribosomes aren't completely stationary either (unless they're attached to something, of course).
Ps. Here's an exercise for you, which you may try out if you happen to have a friend who works at a public swimming pool. Otherwise consider it a gedankenexperiment. You know those floating ropes that separate the lanes in the pool? Try getting your friend to let you into the pool when it's not in use and to release one of the ropes from the walls. Then get in, grab the rope with your arms and legs and try pulling yourself along it. While doing so, try to decide whether it's you or the rope who moves more. (Also, to more closely approximate the Reynolds numbers involved inside a cell, imagine doing this in treacle instead of water.)
By programmable, I suppose you mean that it contains information or can be altered in response to some input or stimulus. The answer is "no" for both. Well, sort of.
Does noncoding DNA contain information? By definition, no. There are probably many regions of the genome that appear to have no information, only later to be found to contain introns, regulatory elements such as enhancers, boundary element, MAR/SARs, targeting sites, etc. Even functional tests (such as removing the region) may not reveal anything because the effects could be minor, or only evident under special conditions. But arguably, if you remove a region and it has an effect on the organism, then it's not really a noncoding DNA, it's just you didn't see the coding before hand.
As for the latter, can it altered, the answer is again "no," or at least "apparently not." Intergenic regions (those stretches of DNA that do not contain obvious or characterized transcribed regions or their control elements) are very stable between organisms and even between species. They seem to have a mutation rate expected for having no information, and thus free to mutate slowly without being swept away. There is no evidence (as far as I know) of any region of the genome being purposefully altered, with the exception of a handful of specific genes whose regulation is controlled by DNA nicking or some such.
Perhaps I am missing your question, being a biologist and not really knowing what a "Turing Machine" is. If I misunderstood, please clarify.