How often does the black market refresh its stock

• The attack is only triggered by enemy movement. Moving on your turn will not trigger Bladestorm (unless your move causes an enemy to move, such as a burrowing Chryssalid).
• No, only the movement will trigger Bladestorm. I've had an Andremedon move past my soldier (triggering Bladestorm), then in a separate action, make a melee attack. The attack was not responded to by my Ranger.
• They happen immediately, usually before the enemy gets to take their action. This is very useful against, e.g. Stun Lancers, which will move into attack range but die before they can actually make an attack. Some enemies, such as Faceless, have a melee range larger than the Ranger's, and don't actually have to move close enough to trigger Bladestorm to attack. (It seems there may have been a recent patch affecting this; it's possible for Bladestorm not to trigger until after the enemy gets to attack.)

The effect of Shield Wall is: you become high cover.

That's it. You don't get any sort of defense bonus, you don't get damage resistance, nothing else. On the bright side, it doesn't appear to prevent you from taking cover, either. The net effect is that you're a regular soldier in every way, except that wherever you're standing happens to count as a high cover tile.