It was perhaps not a direct punishment to Thetis, the golden apple "for the fairest" was found by Hera, Aphrodite and Athena at her wedding and Paris was made to judge between them. His choice of Aphrodite began what would be the Trojan war when the goddess of love made Helen love Paris and follow him to Troy.
Athena was a child by METIS and Zeus. not thetis.
Because Achilles is the child of Thetis and Zeus, and he owed her one.
No, Thetis was the daughter of Doris and Nereus.
Thetis does not promise anything, but Zeus does promise Thetis that her son Achilles will be honored.
Zeus, whose throne Thetis had protected by summoning the giant Briareus when the gods had sought to bind him.
She promises to ask Zeus to side with the Trojans in the battle.
Thetis was promised that Achilles would have honor and glory.
To shjow why Zeus a powerful god would make a promise and help the Nereid Thetis.
The exact answer is Zeus. It was Zeus who wanted to couple with Thetis, but was warned by Prometheus that she would bear a son that would be greater than his father. Fearing for his throne, Zeus gave Thetis up to Peleus, one of the Argonauts. It was at the wedding of Thetis and Peleus that the Eris threw the golden apple. Zeus also selected the judge of who would win the Golden Apple: Paris of Troy. In doing so, he set in motion the wheels that allowed Paris to take Helen as his bride (for giving the apple to Aphrodite, she promised him the hand of the most beautiful woman in the world in marriage). So despite thinking it was Paris' fault, or Aphrodite's fault, or even Eris' fault, in the end, it was really Zeus' fault.
Zeus did not marry Thetis because of a prophecy that stated their offspring would be more powerful than their father. To avoid being overthrown, Zeus arranged for Thetis to marry the mortal Peleus instead, who fathered Achilles.
Hera made Zeus give Thetis to a mortal man as his wife.
Ultimately it was Zeus. Zeus was enamored with Thetis, but received a prophecy from Prometheus that Thetis would bear a son that would overshadow his father. Since Zeus had won his throne by doing exactly that, he encouraged Thetis to marry Peleus, a mortal king. It was at the wedding of Peleus to Thetis that the Golden Apple of Discord was offered "to the fairest". It was also Zeus who chose Paris as the judge of the dispute between Hera, Athena and Aphrodite, which ended with Aphrodite (the winner) giving Paris the hand of Helen of Sparta and making her love him. Since the Trojan War represented the end of the Age of Heroes, it is surmised that Zeus intended to use War as a means to think out the population of heroes and men, as a means to keep mortals in check. The truth is that this was the Apex of Greece. After the Trojan War, Greece began to decline until the rise of Alexander.