What is the ruling on prostrating with the forehead in a shallow depression, such that the middle of the forehead is at the bottom of the depression while the rest of it rests on its edges? Is this considered to be firmly placing it? What if the entire forehead is not firmly placed? Is it permissible to move the forehead without lifting it or lifting it slightly to another spot, even after achieving tranquility?

It is clear from previous questions that you suffer from many obsessive thoughts (waswas), and we advise you to disregard them. Placing the entire forehead on a flat surface is not a condition for the validity of prayer. Rather, prostrating on part of the forehead suffices. It is stated in Al-Ansari's "Asna al-Matalib" that the minimum is placing something exposed from the forehead, and in "Hashiyat al-Tahtawi" that it is permissible to suffice with part of the forehead, even if it is small. Therefore, your prostration on the place you asked about is sufficient for you. The matter is easier than you imagine, so there is no need to move your forehead to avoid empowering all of it, and if you do that, it is a slight movement that does not invalidate the prayer.