#1 is "to do something, and then go", e.g., サルが畑の野菜を取っていく or 鳥が家の前にフンを落としていく. The temporal order of the two actions in the modifying clause is 置く --> 行く (cf. 店員がテーブルに持ってきた水).
As for #2, it's a repeated action. They are serving dishes one after another.