Ubaid period predated Sumer, and was composed of primarily semetic nomads and hunter-gatherers. The language is not specified, as there is (so far),
no indication of written language based on spoken language, older than ancient Sumer.
Old Sumerian is the language used in the Old Sumerian age. A large fraction of texts in Old Sumerian and most of our knowledge on this language is
derived from texts already found before 1900 CE in Nippur, a holy city, the religious capital of Sumer, seat of Enlil, the supreme god of the Sumerian
At some point, in mesopotamia, they had two spoken languages: one for males and one for females. I bet that was confusing for children, who had to
learn two languages from their parents. I wonder if they agreed to speak the same language when at home with their kids.
Old sumerian cuneiforms from Labat:
The Sumerians were the first to write spoken language.
The report that writing in Egypt is older than in Sumer is based on archaeologists in Egypt who use calibrated Carbon-14 dating, whereas Sumerologists
are a conservative lot who keep quoting the conventional 3100 B.C. date for the invention of writing, when it should be 3400 B.C. according to
calibrated C-14 dates.
The last major overview dealing with Mesopotamia as a whole that I know of which collected the various calibrated C-14 dates was that by Mellaart in
Antiquity 53 (1979), with important comments in Antiquity 54 (1980) - these comments acknowledged that the extremely high Mesopotamian chronology that
resulted should be reduced by an average 100 years due to calibrated dates for wood/timber being too high by that average. The end result was still to
support a high chronology rather than a middle chronology, especially for the transition between Uruk IV and Uruk III (AKA Jemdet Nasr). This
transition appears to have occurred around 3300 BC using calibrated dates with the 100 year reduction.
You will also find pictures and discussion of a repertoire of symbols in Marija Gimbutas' publications on 'Old Europe', predating Sumerian. But the
Vinca culture 'writing' appears more to have been tribal or family heraldic emblems like tatoos, found engraved on pots, with no indication that it
represented the words of spoken language.
For so-called writing before the Sumerians, check out works by Alexander Marshack on calendar type markings (Stone Age Europe) and Marija Gimbutas on
the Vinca culture writing (Neolithic Europe). Despite such precursors though, it is clear that Sumerian writing was the first in which there was a
correspondence between the words of the spoken language and the written symbols.