FWIW, the Romans typically cut their wine; it was viewed as uncouth to drink it straight-up. Also, when I think about situations in which wine would be used as “beverage” (as in, this is the only thing you drink, and its for sustenence, not intoxication), I’d suspect they wouldn’t be drinking stuff with the alcohol content we drink. So I vote for “cut” (or, perhaps, only partially fermented).
The Gemara Pesachim 46a states that the maximum time for the dough to remain unbaked without leavening is the time it would take to walk from Migdal Nunya to Tiberias, or about one Roman mile, and Pesachim 93b gives an average day’s journey as 40 Roman miles, so on the assumption that “average” means a day of 12 hours or 720 minutes, the time corresponding to a walk of 1 Roman mile is taken to be 720/40 = 18 minutes.
However, ancient societies certainly did define time-units with precision comparable to (and greater than) the modern minute, even if they couldn’t necessarily measure them very accurately in practice. Base-60 units in Babylonian astronomy included measures as small as 24 seconds. In fact, the “modern” minute itself as a base-60 sub-unit of the hour or 1/24 of a day was used in Hellenistic astronomy, and known to Jewish scholars at least by late Talmudic times (see S. Gandz, “The Division of the Hour in Hebrew Literature”, Osiris 10 (1952), 10-34).