Gokai Changes have no set time-limit but act as a second morphed layer over the Gokaiger suits, in general.
Legendary Ranger Modes are taxing on each Rangers' strength and can only be used for an unspecified but limited time per access, depending on the Rangers' strength. They act as a third morphed layer on top of the Super Mega Mode, which is more resilient.
The Sixth Ranger and Extra Hero keys were in possession of Basco before being taken by the Gokaigers. These were initially used by the core Gokaigers before Gai ever used them.
Sixth Ranger and Auxiliary Hero keys are in the Command Center but only manifest when Orion arrives. Troy notes that Orion is the catalyst to usage of said keys.