The best thing I've figured out about turning eggs is: do not do it too early. You need to wait for the cooked part of the egg to develop a strong texture before it will support its own weight. It's very difficult to turn a floppy, soft egg, where it's comparatively easy to flip an egg that has been cooked more completely on one side. I also use a relatively high heat, as this "crisps" the cooked surface. It also makes the egg more attractive.
The spatula you use can make a difference, also, though I believe this is minor. The spatula you want is a plastic one with a relatively thin, flexible blade. The really heavy spatulas tend to be too tall, in my experience, and push the egg rather than sneak under it.
The only method I have personally found to be reliable for grilling/pan-frying chicken breasts to a relatively uniform doneness is to pound them very, very thin with a mallet or rolling pin. Thin, as in scaloppine-thin, so that it cooks almost instantly in the pan.
Every other stovetop-only method is almost certainly going to produce a bland, tough cut, regardless of whether you press it down or not. As noted in my comment, my usual (lazier) method that does not involve pounding is to get a nice sear in the pan, then jam in a temperature probe and bake it in the oven until it's done (the USDA recommends 165° F, I usually don't go quite that high).
If pressing the meat actually accomplishes anything at all, it would most likely be to just squeeze out whatever tiny amount of precious juices the breast does have, and possibly give you slightly more even cooking on the exterior only; it will not help to cook the interior much faster unless, as stated above, the cut has been pounded extremely thin and flat, at which point it doesn't really matter.
P.S. Salt and olive oil is a terrible "marinade" for any cut of meat, especially a chicken breast. The salt is just going to get suspended in the oil and never reach the meat at all, and the oil itself won't have much of an effect on such a lean cut. You really need to change your marinade as well, preferably to something water-based (or at least not 100% oil).
Best Answer
I generally use about 1cm deep of olive oil when I'm making schnitzel which may or may not be the right oil but it works for me.
I generally find that if the oil is smoking, it's too hot so I tend to get it to a temperature that is very hot, but not smoking.
Once I get it to that temperature, I don't cook too many schnitzel's at once, generally 2 or maybe 3 max to a pan depending on how big your pan is.
The final thing is that you need to make sure you beat the schnitzel out nice and thin before you crumb it so it's only about 1/2 a cm thick when you're cooking it. This way it'll only take a minute or two to cook through and won't overcook the crumb.