"Is it possible that ghosts are just the memories that where left behind when a spirit left the dead to be reincarnated?"
Yes. In fact, I believe that is almost exactly what it is. Rather, I believe a ghost is residual energy. Ghosts that repeat their own actions are most likely chi or some other more physical energy while ghosts that seem to have more of a sense of awareness would be psi or some other mental energy.
The exception to that theory would be the actual spirits that do sometimes stay behind for various reasons. However, their spirit guides will eventually go to them and calm them then help them pass if a living being does not do so first. Ghosts will simply fade as their energy grows weaker over time.
"Are what some people see or feel spiritually just the memories of their or someone else's past life/lives?"
It is possible to have feelings or memories from past lives, however I seriously doubt you would have someone else's memories or feelings from a past life unless they were somehow shared(for example, lovers).
"What knowledge would we possibly gain from knowing of our past life/lives?"
It depends on what exactly you find. You may learn about a soul mate, you may learn what lessons you are meant to learn in this life, you may learn some interesting cultural facts that are lost in time, you may learn of other worlds if you had a life not on Earth, the possibilities are only limited by true history and not just what we know of here on Earth.