100 kg of nails are balanced on the scales with iron weights, the scales are flooded with water, will the scales keep balance under water?

The scales will keep their balance. Under water, the buoyancy force of Archimedes begins to act on bodies immersed in it. The force of Archimedes is equal to the weight of the water displaced by the submerged body. Since nails and weights are made of the same material (iron), then their density is the same, with the same mass, the volume will be the same. The volume of bodies is the same, the force of Archimedes, which acts on these bodies, is the same. Thus, nails and weights will become “lighter” by the same value and the balance of the weights will be preserved.