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2. The translations of the tablets seem implausibly precise. How could we possibly know that a particular bit of ancient Sumerian (or whatever it is) translates as the Anglicized name "Gal Sal" or "Sukkalgir" or (most implausibly) "En-pap X"?"
This is the catalogue data for the tablet: http://cdli.ucla.edu/search/archival_view.php?ObjectID=P0052...
(The fourth drawing is of the two (!) cylinder seals "signing" the tablet.)
Weirdly, the best diagram of the writing I can find is on the cover of The Oriental Institute 2010-2011 Annual Report (http://oi.uchicago.edu/sites/oi.uchicago.edu/files/uploads/s...). (Yeah, just the front page. There's probably an article in there somewhere.)
This version of proto-cuneiform is a syllabary with glyphs representing "KUR", "SAL", "EN", "PAP", etc. (The "X" indicates a missing glyph; there's a chip off the tablet.)
For translation, Sumerian and Akkadian, both in cuneiform, were used for record keeping and official inscriptions for a very long time, at least through the Persian empire. Sumerian, I think, was used as the language of record for a good while even after Aramaic became the lingua franca of the region. (Sumer was a leading producer of skilled information workers, a.k.a. scribes, through the period of the Persian Empire, at least.) I don't remember the whole story of decoding the languages, but there are many multi-lingual inscriptions and literally tons of these tablets, including a lot of student work, word lists, and other textbook things, and letters to people who spoke other languages (see, for example, the Amarna letters).
As for pronunciation, you've got me there. I assume it's by correspondence with other languages that we do know how to pronounce, or possibly by weaker relationships; Sumerian is (AFAIK) unrelated to other languages, but Akkadian is Semitic and Aramaic (and some other languages) are Indo-European.