Are the clips that hold the brake pads in place necessary?

 

Are you talking about the steel clips that slot into the caliper bracket between the brake pads and bracket? Yeah, they are. You'll have a brake rotor stick on or wear your brake pads unevenly.

 

The return spring prevents brake drag.

 

You may want to change the caliper pins at the same time. Mine were worn and I had to go at the brakes a second time to change them later. Good pins help keep the caliper from sticking. Pull the pins and examine them. The finish on mine were worn and uneven so the calipers were a bit sticky. Just something to do if your brakes are still not perfect and drag or make noises. Use silicone grease on those shims for lubrication. Silicone grease for the caliper pins too. Clay