From what I heard, beer was a barbarian beverage, almost as much as drinking milk (as opposed to making butter or cheese out of it) or wearing pants. So if by "lower classes" you mean peregrini, then yes. It might not be cheaper than wine at Rome itself, though. Maybe in Egypt or in the edges of the Empire.
S can never sound like s in "those", it will always sound like the s in "silk". ... but this rule only applies to classical Latin, which is what is taught in school, in comparison to the songs you sing in a choir which are from the medieval period and much different in terms of pronunciation.