What this puzzle takes

Nancy Salomon delivers a very sweet puzzle today, where the theme is united by just one word. It really is dazzling wordsmanship.

Hamburger center - "beefpatty"
Sore throat soother - "lemontea"
Chinese bowlful - "friedrice"
Sweet appetizer - "fruitcup"
Steaming mugful - "hotcoffee"
Word that can follow either half of the above - "cake"

Things to know:
amerind - contraction of "american indian"
Mudville Whiffer - Casey, based on the Ernest Thayer poem, Casey at the Bat.
Daughter of Saturn - Ceres (also Ops)

I think I should know by now who the three sister's are from the Chekov play:
Olga, Masha, Irina