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.
Lining with foil works well with cooking methods like baking or broiling, where the food is not stirred or manipulated much, and so the foil can sit undisturbed.
With stir frying, you are quite likely to break through the foil while doing the stirring, and have to clean up fully in any case. Also, you probably would not get as good a stir fry due the thin layer of insulating air between the pan surface and the food.
This is not something I would try.
Best Answer
If anything is leeching, it would be stuff leeching onto your frying pan, not the other way around. It looks like the spots on the inside bottom of your pan are hard water deposits, maybe combined with residue from food cooked in the pan. Yes, at least in the photo it does have kind of a brownish tint to it, but I don't think it is rust, as stainless steel isn't normally supposed to rust, and the Cuisinart brand has a reputation to maintain. Real stainless steel doesn't leach metal into your food either.
I get a lot of this kind of staining on the insides of my stainless steel pots, especially with boiling beans, for some reason. I think the stains came from cooking activities in the pan, so the they won't poison you if you leave them on. But if they bother you, you can probably scrub them off. I followed the advice of someone on this site about using "Barkeeper's Friend", and it cleans that stuff off great (not Comet, not Ajax, not other abrasive household scrubbing cleanser, but "Barkeeper's Friend." It supposedly has oxalic acid in it, and it dissolves that stuff away with minimal elbow grease. Give it a try,... as they say, test it out on a tiny inconspicuous area first, just to be safe.