Why are siblings unidentical? (Which chromosome of the pair do gametes have?) I know that a normal human cell has 23 pairs of chromosomes (total: 46). On the other hand, a gamete has only 23 chromosomes. Which chromosome does the gamete choose out of each pair? And if "One of each pair of chromosomes comes from the mother, the other from the father.", then the chromosomes of a gamete could be an exact copy of the chromosomes in a grandfather's gamete?

The gamete doesn't "choose" one or the other. Both are made and you get two gametes, one for each.

Also it's unlikely to be an "exact copy" due to recombination and random or independent assortment. There are also smaller influences on genetic variation, and epigenetics, but at this level of question I think you should focus on those two.

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