This is the Special Comissions screen that has the special missions where you can spend AP to obtain reports or Credits. The top button will take you to the missions where you can get EXP reports and the bottom one will take you to the missions where you can obtain Credits.
The Ruins stage is an indoors stage where you will face swarms of little robots with heavy armor. Frontline units other than your tank(s) are not reccomended because they can and most likely will run ahead of your tank, get swarmed and die so try to limit yourself to 1 or 2 tanks at most and the rest damage dealers. Tsubaki, Hoshino and Sumire are good tanks for this stage while Iori, Junko and Nonomi will be great damage dealers for this mode providing great AOE damage. Hifumi also has decent AOE damage while also taunting and grouping the bots using Peroro-sama which can give your team a chance to breathe and heal themselves while the swarm is distracted by Peroro. Serina and Kotama are chosen because their low cost heal and low cost attack buff allows for easy cycling to the skills you actually want to use. For maximum effectiveness, Hoshino will want her T4 bag or she will likely be unusable. Nonomi should have her EX skill at level 3 but other levels can still work.
For the Square stage, you will be fighting a Jack in the box. The timer will reset and the enemy will revive every time you kill it until the stage ends. Recommended units are Mystic damage dealers because the enemy has Special armor and if you lack Mystic units then great Penetration damage dealers like Iori will work to fill in the empty spaces too.