It is recommended to protect the insulation in exterior applications. Painting or Jacketing the insulation are standard practices in exterior applications. This practice will extend the life of the insulation system.
We recommend rubber based pipe insulation over heat tape and to refer to the heat tape manufacturer's instructions for use.
Any pipe with water in it that isn't moving will freeze below 32F eventually. Insulation slows down the transfer of heat, but it doesn't keep it from transferring. It's like having a leak in an air mattress that's impossible to fix completely. As a plumber, I'll tell you that I never see properly insulated (if the pipe or fitting can be seen from any angle, it's wrong) pipes freeze in 24 hr spells of 25F. It never stays that cold here for any longer than that. Also smaller pipes freeze first because they have less mass.
This would be used on the main runs UNDER a radiant slab between the heat source and the zone manifolds (you don't want to lose heat in these supply and return runs). The smaller pipes IN the slab don't get insulation. When I have run insulated hot pipes underground outside the foundation, sleeving it in some styrene to protect the insulation from critters chewing it isn't a bad idea.
Yes. Also heat can leak out of the cold plumbing at a tank water heater, as well as the pressure temp. relief valve. In general, if the hot water hasn't been run for a while, and a pipe or fitting by the water heater is warmer than the ambient temp., it deserves some insulation. I think CA Energy Code say's 5' of H&C plumbing at the water heater as a minimum. Many tank w/h's come with 2 2.5' pieces in the box and a pre-cut piece for the P/T valve . If you chose to insulate all your hot pipes, the hot that you've run to a fixture or area will stay hotter longer, so you'll waste less water waiting for the water to get hot enough. If there is a hot water recirculation loop, the whole thing really should be insulated, and installed with a timer and thermostat also. If cold water pipes are insulated liquid water won't condense on them an turn into mold, rot, mushrooms, or a water source for rodents and insects. This is usually just an issue where either too much moisture or not enough ventilation exists where the pipes are. All pipes that are insulated are more protected from freezing (don't bother with the one coming out of the w/h pressure temp.relief valve, it's an empty drain pipe).