The pivoting part that supports the cylinder is called the crane.
The crane is the short metal arm that holds the cylinder at the forward end. The crane moves to let the cylinder swing out away from the gun's frame for loading and unloading.
Depends on the model. Look in the crane area.
The assembly that holds the cylinder
Butt and inside crane
Check the bottom of the butt and inside the crane.
Butt or crane area
Inside the crane or on the slide
It will be on the bottom of the hand butt, or inside the cylider crane area.
It it has one, it will be inside the crane area.
On a Colt revolver, the serial number is generally in two places. When you open the cylinder you will find the serial number at the base of the frame & crane.
Open the cylinder and look inside on the frame where the crane assembly rests.
Model number will be inside the crane area when you open the cylinder.