If the Rebel is destroyed, the Equipment stays on the battlefield. Similarly, you may pay its equip cost to move it from the Rebel token to another creature you control.

If the ability causes two Rebel tokens to be created (due to an effect such as that of Mondrak, Glory Dominus), the Equipment becomes attached to only one of them.

The copiable values granted by Blade of Shared Souls are locked in as its effect begins to apply. After that point, it doesn't matter if the creature that's being copied leaves the battlefield or if any of its copiable values change.

The creature copies exactly what is printed on the chosen creature (unless that creature has additional copy effects affecting it, is copying something else, or is a token; see below). It doesn't copy whether that creature is tapped or untapped, whether it has any counters on it or any Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, or so on.

The Rebel enters the battlefield as a 2/2 creature, then the Equipment becomes attached to it. Abilities that trigger when a creature enters the battlefield see that a 2/2 creature entered the battlefield.

Non-copy effects that have already applied to the equipped creature will continue to apply to it. For example, +1/+1 counters on it will still affect it.

If the target creature is a token, the equipped creature copies the original characteristics of that token as stated by the effect that created it. If the equipped creature isn't a token, copying a token won't cause it to become a token. Similarly, if the equipped creature is a token, copying a nontoken won't cause it to become a nontoken.

If the target creature is a double-faced or melded permanent, the equipped creature copies the face shown. If the equipped creature copies a melded permanent or the back face of a double-faced card, its mana value is 0.

If the target creature is copying something else (for example, if that creature is equipped by another Blade of Shared Souls), then the equipped creature becomes a copy of whatever the target creature copied.

If the target creature isn't normally a creature (for example, an animated Monument to Perfection), the equipped creature will become a copy of the noncreature permanent. Blade of Shared Souls will become unattached and the copy effect will end. The previously equipped creature will revert to whatever it was before the copy effect applied.