Chicken – grill a chicken/turkey breast in the night and eat it 12:00 and 18:00

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).

Yes, this technique will give you approximately the same results as Nando's. You want to use an oil with a relatively high burning point like sunflower, rapeseed or groundnut - olive oil may burn.

Another point to remember is that Nando's chicken breasts all have the skin on: this adds flavour and helps keep the meat moist. For the best results, both in terms of not giving yourself food poisoning and avoiding dry chicken, use a quick-read digital thermometer to ensure the breast is only cooked as much as it needs to be, but at a safe internal temperature. It should reach 75ºC in the thickest part.