I have had 2 wood burning fireplaces like that over the years in the various home I lived in. The panel are held in place by the "Z" clips like you see in one of your pictures. The fireplaces I had used the clips on all 3 panels. It seem your rear wall is missing them, since it is tilting over at the top. The screws are simply drilled through the sheet metal that hold the clips in place. You may with some care and a good light, see where the clips were at one time. If it never had them, it needs them now. They can be added after the fact. There is no magic to get them to do what they need. Use the spacing/placement that the other clips have from the ends to either locate the old holes if it had them before, or use that dimension to add new ones.

The panels are one piece on each wall and bottom, and reinforced with a fiber so when it cracks it will not readily fall apart. Mine cracked every year, I replaced them every year too. They should be removed periodically and cleaned behind them, removing the ash that collects under the bottom and behind the walls. Ash is corrosive and will degrade the coating on the walls of the firebox.