From the standpoint of modern molecular biology, one can say that the table in the Wikipedia article would be better if — in the first instance at least — it left blank the entries for the ribonucleoside corresponding to the base thymine and the deoxyribonucleotide corresponding to the base uracil. This is because the thymine ribonucleoside is not a normal constituent of RNA, and the uracil deoxyribonucleoside is not a constituent of DNA.
It would also be more honest if the article explained that the abbreviations used in DNA and RNA databases employ the single letter to represent a deoxyribonucleoside monophosphate residue or a ribonucleoside monophosphate residue, as the case may be, and that only the chemist or student of nucleotide metabolism is likely to be concerned with the abbreviations presented.
It is in metabolism (for which these were named) that the abbreviations make sense. ATP is adenosine triphosphate, so the ‘A’ has to represent the nucleoside, adenosine, and dTTP, deoxy-thymidine triphosphate, is the metabolite that is a DNA precursor used by DNA polymerase. The reason that dU justifies inclusion is that dUMP exists in cells — as a precursor of dTMP (which is then converted to dTTP).
So finally to your Q1 about 5-methyluridine. The answer is that, as far as I am aware, this does not occur in cells as the free nucleoside or the free related base or nucleotide. It can only be considered as occuring at a particular positions in certain transfer RNAs (and ribosomal RNAs) where it is produced by the enzymic modification of the uracil ring by a 5-methyluridine methyltransferase. So in the metabolic era, before the detailed chemical analysis of minor bases in structural RNAs, there was never any reason for biochemists to refer to 5-methyluridine and consider its abbreviation.
You may or may not be aware that there are many minor bases of this type in different tRNAs, all produced by enzymic modification of the four bases occuring in an initial RNA transcript synthesised by RNA polymerase. There are over half a dozen different modifications of uracil, so it was far more meaningful for the scientists working on them to distinguish them with abbreviations that indicated their chemistry, rather than assigning arbitrary single letters to them. The fact that one could logically employ T as an abbreviation for 5-methyluridine would have been of no practical use, and, because of the association of thymine with DNA, could well have led to confusion. Hence, the committee standardizing nomenclature would have been faced with a fait accompli. In such circumstances realism prevails over idealism. (And in any case the names of the bases are a mess — how many students have been confused by adenine/adenosine but cytosine/cytidine.)
Regarding your second question: people don’t talk very much about m5U and U, but when they do they naturally distinguish between them because they are different molecules. Specifically, the databases for tRNA structures will distinguish clearly the different modified bases.