I doubt very seriously if the failure of the humidifier supply tube is a result of heat. First of all, let us consider the temperature of your incoming cold water supply. The mean average of the earths crust is 55degF (geothermal temperature of the crust). Soil is a rather poor insulator so the surface soil then cools proportional to the ambient air temperature. While the crust is 55degF the actual surface of the soil will freeze for a short depth which we define as the "frost depth". While the frost depth is the deepest point at which freezing commonly occurs it must be understood that from that depth the temperatures increase gradually from freezing temp(32degF) to the natural geothermal temp(55degF). Typically geothermal temp occurs at approximately twice the frost depth. In order to protect our water lines from freezing the codes require that we bury the line 6" below the frost line thus when the dirt is frozen to the frost depth the average temperate at the water line may be only slightly above freezing (34degF+). Fresh water reaches a maximum density of 231cu.in per gallon at 39degF. There is a very coplex formula to determine the rate of linear expansion but for the sake of illustration let us use the maximum here. When water is expanded from its maximum density of 39degF to the boiling point it expands by approximately 40:1 thus we could say the physical volume of a 40gal. water heater expands by one gallon. To put this in perspective consider that a 1/2" pipe has a volume of one gallon for each 98 linear feet. We must now keep in mind that water is not compressible therefore as the volume expands it must go somewhere. Normally the increase in volume is compensated by physically pushing some of the water back to the municipal main or to your well pump pressure tank however if we install a check valve in the line there is no place for the additional volume to go. In this case the excess volume would by necessity be relieved by discharging through the water heater Temperature & Pressure Relief Valve (T&P valve) BUT let us consider another potential problem here. Imagine for the moment that your T&P discharge line discharges out through the wall of your house. The discharge end of the line is then exposed to atmospheric temperature and in a worst case scenario the outside end of that line could freeze shut. At this point there would be no place for the additional volume to be released and it could result in blowing out fittings or valves or rupturing a pipe or the water heater vessel. Now keep in mind that the T&P valve is a spring loaded valve that is set to release when the pressure reaches 150psi and most likely the plastic line to your humidifier is failing slightly before the internal pressure is sufficient to release the T&P valve. On the other hand, if you did not have that plastic line there is a very strong likelyhood that the increased volume could be relieved by blowing out a compression fitting at a fixture angle stop, a pipe joint might fail or premature failure of Bibb Washers in your faucetts. The proper solution is to install an expansion tank on the water heater side of the check valve to absorb the increased volume. Installing an expansion tank is quite simple. You simply install a Tee on the cold water line with a male thread adapter on the Tee stub out, then screw the expansion tank onto the thread adapter.

What remington said, with a couple of exceptions/additions: Dissolved solids is not the same thing as turbidity. Turbidity is a measurement of clarity and is caused by suspended (non-dissolved) solids and colloidal materials. You want test results from an independent lab to get ACCURATE numbers. The sales folks that come to your house from the various vendors will use field tests that can be very accurate in the right hands. However, most of those folks use poor technique at best and will be well off the actual numbers. You city water report can be a good resource for you as well. Be aware that the water can pick up a few things on its way to your home, particularly iron which makes a huge difference when specifying a softener. You want to know: pH, TDS (total dissolved solids), iron, manganese, chlorine/chloramine (I assumed city water based on your description), hardness, alkalinity, particulates (if you have them in your water you want to know amount and type). Does your water have an objectionable odor or color? Do you see rust-colored staining in toilets, showers, sinks? You do not want to water your yard with sodium-softened water. Your grass/plants will not thank you for it. This leaves you two options. 1) As you mentioned, plumb to your outdoor faucets with untreated water, 2) regenerate your softener with KCl (potassium chloride) rather than NaCl (sodium chloride). KCl is more expensive, plus you will be treating alot more water. If you have a way to determine how much water you use indoors vs your total water bill, we can give you an idea what the cost difference would be. Water softener providers: Kinetico, as you mentioned, is good. They do tend to be the most expensive option. Their equipment is reliable, sales people are generally well-trained, and they do not require electricity. Other national vendors such as Culligan are good. They sell reliable equipment, but sales people are generally less well trained. Local vendors are well worth your time. Their prices are typically good and they have access to the same reliable equipment (Fleck valves) as the big guys, but often with more personal attention and better prices. Once you have test results and a few vendor quotes, we can help ensure you get a correctly sized softener if we know the following: 1. Test results 2. # of people in the home 3. # of bathrooms 4. Any high-water-use items such as pools, jacuzzi tubs, mult-head showers? 5. Frequent guests? There are a few things that you want: 1. 10% crosslinked resin (to resist chlorine) 2. gravel under-bed 3. top basket 4. USA-made resin (higher quality and better size control) 5. fine-mesh resin IF you have iron, standard if no iron 6. Fleck valve or equivalent 7. Anyone who gives you a quote should perform tests. 8. If a vendor is not responsive before the sale, they will be less so afterward.

For the sodium issue it depends on how hard your original water is as to how much sodium is in it. Our water starts at 15 grains and so has around 120mg of sodium per liter. That's about the amount in a slice of bread. The harder the water, the more sodium you will have in the softened water. We can't taste the sodium. And we have a family member who is on a low sodium diet and dialysis. Her doctor said that amount of sodium was not a problem for the level of sodium in our water and her particular medical history. So it's worth checking with your doctor if that is the only issue.

The plumbing for this type of sink is decorative and functional, not the junk you were given. If this is a new build, your GC should be involved in this and you should not be dealing with the plumber yourself. I would talk to the GC and complain about the installation being inappropriate for the supplied sink fixture and ask whether he is going to make it appropriate or give you a discount for doing that on your own later. I do believe I have also read about pex not liking UV light and that should be a simple google for you to discover. Use that info to get the GC to pony up for a good plumber, or to pay for the repair after the closing. If you can get them to give you stubs, the correct plumbing in the finish of your choice is available from places like Vintage Tub and Bath. You can keep the supply coming from the floor. I see it in Satin nickel here on Houzz, but not brass. Vintage Tub and Bath has 30" high water supplies that go through the floor that are meant for a bathtub, in polished brass. With turn-off valves and escutcheons for covering the floor hole. Click on the "specifications" link and you can see how they connect to your pex. Cheviot straight supply lines.