How do you place mines? What damage value do they have when placed? Do the suicide squad take damage when they attack with mines directly?

The soldiers don't actually "place" the mines, they just attack. The mines are just a range 1 weapon with a limited number available (5 boxes to check off on the stat card). The soldiers won't take any damage from their mines as well, but they definitely will take damage from attacks while they move into range to use the mines. That's where the "suicide" aspect comes in: They have to get really close to the enemy to use their mines.