Chicken – Condensed cream of mushroom over chicken and rice

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).

From your description, these are IQF (individually quick frozen) chicken parts. They are blast chilled at the processing plant, before being put together in the bag. They don't stick together because they are so cold that there is no liquid water make them stick.

You can repackage them into any freezer safe set of packages that you prefer, in portion sizes that you prefer.

I suggest using small zip-type freezer bags, with one meal's worth per bag. You definitely want the type that are rated as freezer bags, as they are less permeable to gas and water vapor, and will keep the the contents in the best condition. You can squeeze out the excess air, but I think using extra foil or trying to suck out air with a straw is more than you need to do.

(If you really want to ensure there is minimal air, place each bag in water after you fill it, letting the water squeeze out the air, so you can zip it up.)

If you use place all of the small bags in a much larger freezer bag or a sealable freezer safe plastic container, you should get very good protection for each piece, while still being able to use them in small portions.

The extra layer is just for additional protection, it is not strictly necessary.