"una" = "a" (English) and "a" in English can equal "one", "vez" = "time" , "one time" = "once", "al" = contraction of "a + el" often the Spanish "a" or articles like "el" are not translated. Not sure how there used here but "una vez al día" = "once a day" I looked it up. One use of Spanish "a" is as "per, every" in this case it is "per". "per" = "a" in English. The "el"(in al) is dropped because we do not use "the" before "week" like this("one time a the week") but just as it is odd to use in English it is equally odd for the "el" not to be in the Spanish sentence.
Literally it's "to the day" which is less commonly used in English but still exists ("Those apples are two dollars to the pound" or "My car gets 40 miles to the gallon"). To say "per" would make this sentence "Ela bebe vino una vez por día" which would mean the exact same thing but with slightly different phrasing. Por is used for per in this sense, as in, cincuenta por ciento (fifty percent or fifty out of a hundred).
I heard people in Ecuador pronouncing the D sound between their teeth quite often. My little host sister even showed me how to pronounce "ciudad" once and she told me I was wrong until I stuck my tongue between my teeth on the final d. lol. They didn't do that with the C sound though.