Regarding a new home in HH climate (2B) with non-vented attic. All ducts and pipes are within the conditioned space. No pipe in exterior walls. Copper pipe was used for pressured water service (1″ and below), and it’s routed overhead (attic, between floors, etc).

I insulated the hot water pipe with 1/2′ thick polyethylene foam split tubes for energy conservation.The seams are sealed with self-sticking adhesive. The ends and fittings were sort of haphazardly taped with PVC tape.

I was thinking of insulating the cold water pipe in a similar manner just for noise control.

So here’s the questions:
1) Does insulating the cold pipe make any potential condensation on the outside of the pipe better or worse? —assuming its not totally 100% covered and sealed, and has no vapor barrier.
2) Is a vapor barrier necessary? Just by comparison, my HVAC ducts have insulation with a silver colored cover (vapor barrier) to avoid condensation. Does that same philosophy/concern apply to cold water pipes. I realize that the air conditioned ducts will run cooler than the water supply in the summer, but in the winter, the water pipes will be much cooler than the heated house.
3) Which is better to use—tubes of foam polyethylene,or tubes of foam rubber? Or something else?