The salt adds flavor, but it also helps reduce the gelation of the starch in the pasta. The starch in food is the form of microscopic grains. When these grains come into contact with water, they will trap some of it (think cornstarch in cold water), but when the water is hot they swell up like balloons and merge with each other, and you have starch gelation.
Another thing you may want to add to the pasta water is some acid (lemon or cream of tartar). Tap water in most cities is made alkaline, which increases the starch loss from the pasta to the water, making the pasta stickier.
You've got a great pan and in a short time I'm sure you'll come to love it.
When using a standard pan (one without non-stick coating), heat your pan dry over high heat until you can hold your hand about 6-inches above the cooking surface and feel the heat radiating upward. This allows the tiny cracks and crevices that are imperceptible to the bare hand to expand and when the oil is added, it will coat and create a more even cooking surface.
Add just enough oil to lightly coat the surface. Adding to much oil leads to pan-frying which is fine if you're frying chicken but not what you want when searing and sauteing meat. There should just be a thin film across the bottom of the pan. An additional benefit to first heating the pan is the fact that it will actually take less oil to coat the pan due to the decreased viscosity. When the oil hits the hot pan it will instantly heat and should shimmer across the bottom like water on a freshly cleaned windshield.
You don't put the oil in the pan first because the longer oils and fats heat the quicker they break down and smoke. If you were to add cold oil and cold food to a cold pan and then start heating, you just end up with a big sticky mess.
Make sure you're prepared to add the food to the pan once the oil goes in otherwise the oil will start to burn.
The issue with burning and overcooking is going to be a matter of controlling the heat. Start searing and sauteeing over high heat because as food is added it will suck a good deal of heat from the pan. If it isn't extremely hot to begin with you'll end up with a steaming mess of gray colored meat or vegetables that aren't doing much cooking. Once the meat is browned but needs further cooking you can always turn down the heat to prevent excessive browning and crusting before the interior is done.
Even if you aren't planning to do a pan sauce, or if you've burnt what was cooking in the pan, you'll still want to deglaze with some water while the pan is hot (you can reheat it if it has already cooled down) so that you can scraped up the cooked on bits more easily and have less scrubbing to do when cleaning the pan.
Best Answer
Chemically the pits etched in your pot are the absence of the stainless steel material that makes up the pot. In other words the white spots you're seeing are where a small amount of the stainless steel has been removed from the surface of the pot, much like it had been scraped off. So the pits are completely harmless because they're not actually any kind of chemical substance.
Chemically what causes the etched pits to appear is that the chlorine from the salt attacks the passive film of chromium oxide that normally protects the surface of stainless steel. Stainless steel gets its corrosion resistant properties through the addition of chromium. When exposed to oxygen the chromium in the steel oxidizes and forms a very thin layer of chromium oxide on the surface the metal. This layer prevents oxygen from going further into the steel preventing it from further oxidation (rusting).
Normally stainless steel isn't harmed by salt dissolved in water or by the chlorine found in tap water. However things are different when a grain of salt sits at the bottom of a pot. It will dissolve into chloride ions (along with sodium ions) that are concentrated against a small spot on the surface of the pot. What exactly happens then isn't entirely clear, I've read conflicting descriptions, but the reaction seems to reinforce itself causing the chromium oxide layer at that spot to be removed. This exposes the steel underneath to damage by both chloride from the salt and oxygen dissolved in the water.
(The Chemistry Stack Exchange has a question on how chlorine attacks stainless steel if you want a more scientific explanation.)
There's really nothing you can do or need to do fix the spots at the bottom of your pot. You can't remove something that's not there. A new chromium oxide layer has already formed over the pits and your pots is as corrosion resistant as before.