Is the cladogram pictured here correct? Does it accurately represent the cladistic relationships between these species based on their derived characteristics? Why or why not?

The cladogram is correct.  The further explanation is given below.

Explanation:

As with most other species excluding lamprey, paired arms and legs are established. In any organism except lamprey as well as tuna, paired legs become available. Throughout all animals, except lampreys, tuna, certain bullfrogs, the amniotic membrane seems to be preserved. In kangaroos, rhesus monkeys including people, mammary glands were only ever available. The placenta has only been found throughout rhesus monkeys and also in humans. Foramen magnum forward will be exclusively found in humans.