Increases solubility? Why is it HCL?

Magnesium becomes a solid when it reacts with the OH- ion to become Mg(OH)2. When you add HCl, the H+ ions react with some of the OH- ions to make water. Since there are now fewer OH- ions in solution the equilibrium shifts to try and compensate and bring the concentration back up. The only way to bring that concentration up is to dissolve more Mg(OH)2.