1. parents got their chromosomes from your grandparents, and so on. but are the chromosomes that are passed along through the generations exactly the same?
2. is your maternal chromosome exactly the same one that your mother received from one of her parents? explain

1. No, the process independent assortment randomly segregate the maternal and paternal chromosomes to different gametes.  

2. No, the process of crossing over generates recombinant chromatids.

Explanation:

1. During anaphase-I of meiosis-I, the random segregation of maternal and paternal chromosomes to the opposite poles of the cell occurs. This process randomly distributes the homologous chromosomes of a pair to the gametes. Therefore, the progeny obtains some new combinations of maternal and paternal chromosomes that were not present in their parents. Further, the process of random fusion of these gametes adds more new combinations of chromosomes.  

2. The process of crossing over generates the recombinant chromatids during prophase-I. This produces some new allele combinations on the chromosomes which were not present in the parental chromosomes.