Can you equip an equipped equipment? Like a Spinning Axe, can I change its target?

No. While Spinning Axe is attached to a unit, its Equip ability is inactive — attached cards' printed rules text is turned off — so you can't pay [A] to re-target it (Rule 718.2; FAQ #6999).

To "change its target," the gear has to be detached first: if its unit is killed or recalled, Spinning Axe detaches, returns to your Base ready, and you can Equip it to another unit. Effects that let you move already-attached gear (Weaponmaster, Jax's Legend, etc.) explicitly say so — plain Equip doesn't.