GodGinrai is correct- Wine is incorrectly translated directly- also, cocktails should be the word used in some places as well. I imagine the japanese states "sake" which encompasses a WIDE variety of alcoholic beverages by the single word. Were this series to get a full time translator, it won't be easy to get everything right without doing background research on some things that come up- even the group that did Bartender had issue with translation (and that series certainly went overboard with apocryphal and made up stories about alcohol/cocktail origins and the translators went above and beyond trying to parse all the info).
For instance- Angostura bitters are a Bitter- not a wine, a whole different class of cocktail ingredient. Drambuie is a Liqueur- it is made from scotch in part, but it is a liqueur- while it can be imbibed on its own, it is often used as a cocktail mixer ingredient. (also, different than Liquor.) The Shochu she made with the flower is an infusion- and again, it is not a wine, since it is originally a distilled product.
As for the nature of cleaning the cart glassware- much like food trucks, most mobile operations that require water/cleansing setups find a storage solution to water to bring along for their daily use. Also, many cocktail bars (and in particular some japanese styled cocktail bars) do not use on demand running water to clean- there is a setup with multiple basins/sinks to have washing/rinsing specifically with water for each alloted already, even in brick and mortar shops.
All the best if you choose to follow up on this manga- certainly a gimmicky conceit but always enjoyable to find more food/drink related manga out there.