(1)They mined the desired effect——as an actor might.   

as an actor might 是方式状语从句（它是比较状语从句的一个子类）。等于：as an actor might do.    

(2)The more you can come to accept others as who they are, the more you can move forward with your goals regardless.

as who they are 是accept 的宾语补足语。as 是介词，后面接名词性从句who they are，作as 宾语。     

(3)The news showed a trick of cheaters and, to my surprise,it was the same situation as I had experinced during the day.

as I had experinced during the day 是比较状语从句，照应主句的the same。其中，as 是“比较代词”，引导从句的同时，又做了experinced 的宾语。