One:
I disagree with your stated use of L2. L2 collects the vertical growth of the hanger nodes. This number plus the weight from L1 are used to select the hanger. Deadweight sag can affect the vertical growth around +Y restraints. The most complete mothod is to include weight and estimates of hanger load in L2. You might get the same results without Weight but not always.
Two:
Include F1 if F1 describes a sustained load. Do not inlude F1 if F1 is an occasional load.
Three:
Enter your predefined load as the Operating Load in the hanger design input.
Four:
Cold spring should not affect the hanger selection. Do not include "CS"in your hanger design load cases (L1, L2 & perhaps L3). There might be some interaction between +Y supports and vertical cold spring. If so, you may have to override the program's automatic hanger selection with some hand calculation.

All my comments relate to the curent version of CAESAR II - Version 5.20.