Does the 30 .in x 60 .in shower system come with a right hand drain that will fit an existing drain that has approx. dimensions of 16 .in x 10 .in ?

The 36 .in x 60 .in kit is designed to fit where a tub used to be, and hook into the existing drain (16 .in x 10 .in from walls). Note, there is no 30 .in, only 36 .in x 60 .in.