Do all the gametes formed from a parent organism have the same genetic composition (identical DNA copies of the parental genome)? Analyse the situation with the background of gametogenesis and provide or give suitable explanation.

No, all the gametes formed from a parent organism do not have the same genetic composition.
Sexual reproduction in organisms generally involves the fusion of gametes from two different individuals. These gametes form by the process of gametogenesis. In the heterogametic species, gametes are of two types namely male and female. Gametes are haploid though the parent body from which they arise may be either haploid or diploid.
(a)  A haploid parent like Monera, fungi, algae and bryophytes produce gametes by mitotic division. The number of chromosomes, i.e., the genetic composition remain same after such type of division.
(b)   The diploid parent like pteridophytes, gymnosperms, angiosperms and most of the animals including human beings produces gametes by meiosis. In such organisms (diploid), specialised cells called meiocytes (gamete mother cell) undergo meiosis.
At the end of meiosis only one set of chromosomes gets incorporated into each gamete. It means the gametes formed contain a haploid number of chromosomes in contrast to the number of chromosomes in mother cells.