Although purgatory is not found in the Bible, references that appear to allude to it are found in the apocrypha books which the Catholics also include in their bible. Further, they rely on revelations of their popes for religious beliefs and practices, making it a christian religion that doesn't just go by their Bible. I do not think that the Catholics see their purgatory as anything but an atoning for sin spot where the soul moves onto heaven after it is complete.

As for reincarnation, there are various viewpoints on it, all equally valid since non of the views has been proven to be more accurate than another. As you point out, there are some that think you suffer in this life because of a past life, hence the old saying "I must have been such a bad person in another life". But other systems don't look at reincarnation as a means of punishment because of a former life, but rather a means of progression towards an ultimate being fit only for the spiritual world. Others look at it as we come back by choice, but are not forced into reincarnation. Maybe we are adventures and there was still things we wanted to learn and experience here (bad past life or not). There probably are other views but far be it for me to think of off the top of my head.