How does ‘bladestorm’ work

xcom-2

One of the ranger's abilities is Bladestorm. The description is:

Free sword attacks on enemies that enter or attack from melee range

I have some questions about the mechanics:

If my character is the one moving, do they still get a free sword attack? Or only when the enemy moves?
If an enemy enters melee range and then attacks, do I get two free sword attacks?
Do these free sword attacks happen immediately on the enemy's turn? Or do I need to wait until the next turn to the use them? If I have to use them manually, do they stack?

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.)