The first story is one of the best in the animated series. An alien probe arrives at Earth, sends a message back into space and then self-destructs. The Enterprise is tasked to follow the path of the message to determine who the recipient is. They encounter Kukulkan, an ancient Mayan god. He has waited centuries to be summoned back to Earth and he is angered at not getting the attention that he feels he deserves. He tests the members of the Enterprise crew and they pass. Kirk and group also free some other creatures held by Kukulkan and during the melee Kirk risks his life to save Kukulkan, demonstrating that he is in no way a god. Although this is one more instance of the well-worn ancient astronauts theme, it is so well done that it would have made an excellent Star Trek movie.
The second story is much weaker. The Enterprise is pursuing another ship and they are pulled through a supernova to another universe where time moves backwards. All the members of the crew start getting younger, so even though they determine a way to get back, they growing youth of the crew leaves them dysfunctional. Fortunately, the Enterprise was carrying two elderly passengers who are experienced Star Fleet officers. They take command when Kirk and Spock are incapacitated and guide the Enterprise back to normal space. The members of the Enterprise crew are then passed through the transporter and restored to their previous state.
The problem I have with this is that if the transporter were capable of acting as a "fountain of youth" then everyone would use it on a regular basis. There would be no aging, valued officers would be kept in their prime and the world would stagnate. This obviously has not happened, so the episode suffers from a major logical flaw. Furthermore, since some of the Enterprise crew would have de-aged beyond their birth, to get them back, the transporter would have had to recreate them from their stored patterns. This would have literally been creating people from nothing, a plot