龙舌兰 means tequila because it refers to the agave plant. 龙舌 - dragon tongue, 兰 - orchid (and a lot of other plants). in 兰姆 the "lan" is used phonetically, to make the first syllable, the "ru" of "rum". in 龙舌兰 the 兰 is used botanically

Kim's drink is a shot of gin, because the Korean family name Kim is written with chinese characters as 金 which in mandarin is pronounced Jin and is the phonetic character of the alcohol gin

The phone call to your ex-wife is apricot scented beer, I think

The borscht is too blurry for me to read well but I think it's aged vodka(?), tomato juice, carrot juice and black pepper