1) Is inter-species reincarnation possible? Do you think a soul can be reborn in a different species?
I do believe it is possible, though I don't think it is frequent. Among those of us Jews who believe in
gilgulei neshamot (reincarnation), one of the reasons for it that is sometimes given is to give a person a chance to fulfill certain commandments that they did not adequately fulfill during their lifetime. So there are certain chasidic stories about people who came back as animals to help a family member or friend, or to be a comfort in a time of need, or even to hear words of Torah being spoken.
Growing up, we had a cat that we speculated was a
gilgul (reincarnated person), because it would leap up onto the table whenever anyone was studying Talmud, and sit, staring into the page of Talmud, purring. It didn't care at all about other books or other kinds of studying, just Talmud. Did a few other strange things, too. Likewise, a friend of mine went to a certain yeshiva (advanced school of Torah study), and there was a small dog that was in the habit of coming into the study hall every day for the lecture, during which it was completely quiet, and just lay there listening. My father says that when he was at yeshiva, there was a cat that came in every afternoon for the afternoon prayer service: it stood for the Amidah prayer (which is said standing), and it left after the Kedusha section of the prayer, when it is permissible for people to begin coming and going from the sanctuary.
So I think it can happen, but I don't think it happens to everyone.
2) How long after death does it take before someone is reborn? Instantaneously?
I believe it is not instantaneous, though how long it is I believe varies. I think in between each life, we have the opportunity to step aside, as it were, with full knowledge of all our lifetimes, evaluate ourselves and think about how we're doing, and what we still need to do, and how we feel about it all. For some people, in some instances, we may choose to dive right back in, and get reborn right away. For others, in other instances, we may take a little time before we get back to it.
3) Do souls choose their own incarnations?
I think of it more as a cooperative process: people get a say in their incarnations, but not necessarily a final say.
4) Are new souls being made now or are all of the souls already created and reused?
I tend to think that new souls are constantly being generated. I think the vast majority of souls created do get re-used, so to speak, but between population growth, some souls taking the option to decide that their need to reincarnate is over, and not all souls reincarnating simultaneously, there is room for the addition of new souls.
5) How much of this individual will relate to his or her previous lives? Like, is the personality going to be the same? Or an entirely new personality is created and only the consciousness is passed on?
So why do we have no memories of past lives? Often people say that reincarnation is so the soul can experience as much as possible. But if these memories are erased each time we move to another body, and start from square one, how can it count as experience?
I think when a person is incarnated within this world, their mind begins as a tabula rasa. The knowledge of the soul is not the knowledge of the physical mind. That said, I do think that sometimes certain strong memories or strong ideas or desires contained in the soul can effectively become something like a primal unconscious, never (or almost never) rising to the awareness of the incarnated person, but acting like deep, deep subconscious impulses.
If a person remembered everything (or any significant portion) of their past lives, or carried over whole personalities, much of the effective point of reincarnation would be lost. I believe that the primary reason for
gilgulei neshamot is to give a person a chance to "balance their cosmic scales," by countering the unresolved negative acts they did in previous lifetimes by doing positive acts in succeeding lifetimes. Secondarily, it is to afford the person the chance to do whatever thing or things are their task as part of the divine plan, but to do those things purely out of free will, from their own desire to do those things for their own reasons (thus reconciling human free will with having a concept of a divine plan). Tertiarily, it is to afford the person chances to learn wisdom, compassion, mercy, lovingkindness, humility, awe, etc., and then to teach those things to others.
(I should add that I believe that sufficient learning of those qualities over successive lifetimes strengthens their "weight" in the makeup of the soul, so that eventually, after having truly internalized those qualities over several [or many] lifetimes, the soul when reincarnated will more potently drive the developing mind and personality toward those qualities in life.)
This last question isn't exactly personal: In reincarnation, if you can't clearly remember your past lives, and you can't notice reincarnation, what exactly is being continued if not the memories? Wouldn't you agree that our souls are constructed by memories?
No, I think the soul contains memories, but it is not constructed of memories. The soul is made of
shefa (divine energy) and spiritual energy, and is powered by a tiny spark of divine manifestation. That energy construct contains the memories of all our lives, and over time develops an overarching super-personality independent of any physical lifetime, but made up in part of a composite of the personalities of all those lifetimes fused with the soul's experience outside the physical universe.
When the cycle of reincarnation is complete, and the soul has no unresolved negative acts, only a large "balance" of positive acts to its "credit," and the person has learned and taught and contributed to the world and fulfilled their part of the divine plan, I think they can choose-- and eventually all choose-- to move on to Olam ha-Ba, the World To Come (more or less like Heaven). The soul as it exists in Olam ha-Ba is this composite soul.