Do you think: In our next life will we have to start back at square one with our research & remembering?
Its my understanding that each life we have has its own goals and parameters. We decide before each life what we will know and what traits we will have, etc. Thats not to say we won't be born knowing or have or not have a desire to search out answer about our lives. Do you feel your knowledge today is a product of what you have learnt before about past lives?
Or will we retain what we have learned about our past lives?
If we do it will probably be something we know instinctively, but do not know why. Sort of like how people know how to play the violin at an early age, or have the ability to pick up the violin quite easily.
Do you think because we have made our PL's we remember so important to us this time, we won't remember the same PL's again?
According to Brian L. Weiss, certain lifetimes stick out because of unresolved issues. Once resolved, these lifetime will simply fade from memory, at least, from the conscious state; never from the subconscious. I believe we also remember lifetimes that were important, happy times, etc., not necessarily traumatic. I have many memories, starting from when I was a child, but I never found any traumatic. None caused nightmares. Many are quite pleasant, although a few were unsettling.
Or instead will we only remember different PL's that we have not yet remembered?
I suspect most of us have had hundreds of lifetimes. I do believe, that "other" lifetimes will emerge if they are events that have unresolved issues, regrets, pain suffering, etc. You may have only decided to work on a few lifetimes in your present life. This could be for several reasons such as paying off karma to a certain other soul who is not available for a lifetime with you at this time. So instead, you decided to workout something else from your past.
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Past life memories can serve all sorts of purposes in a person's life from helping to understand how our universe (and dimension) works, to paying off karma, to serve as a warning, or as a reminder about something you need to focus or work upon.
In the end, I wonder what the purpose is too. If we start over again, from scratch, so to speak, why go through all the trouble. However, I think its because each and every lifetime is significant and serves a purpose. But with that said, I have read in many books over the years stating that older souls have a problem with the constant repetition of relearning and redoing things from one life to the next. Going back to school, from grade 1 to 12 is a pain (that is how it felt to me... it felt like I had done this already a few times; I am sure that may pose a problem for some students, especially those who died young in several lifetimes). Still... we soldier onward.