Hey here are some more little thought or headcanons I have. Hope you enjoy.
Amanda/Nyota necklace.
Sarek gave Amanda her necklace as a birthday present while is was pregnant with Spock, although Vulcan do not celebrate them, the blue mineral was like the water on earth. He will have denied the little smile he had he see his wife so happy.
When Spock left for star fleet Amanda gave to it him so he could always remember that she is proud off him. He always wore it under his uniform and on the day she died.
He gave it to Nyota a few weeks after Khan.
Why Carol was on board after York town.
Since her father had past away the only family she had was her grandma, when they had boarded at York town a message had come to say that her grandma had taken seriously ill, the place it as a few weeks to live... she left on a shuttle to earth as so as she could.
Jaylah backstory.
On Jaylah home plant the trees are different shades of purple, her father worked on a intergaxlay mining vessel. Her plants was a peaceful one, she was nine when she when on her father's minning ship her mother stayed with her two little brothers.
It was so much fun, until a distress signal form a plant come up on the computers the when to see what was wrong.
Her and her father we stuck there for three just until there planned to escape. In was another twelve years she was free.
Gaila.
Gaila just stats in engineering for two reasons usually something goes wrong and the other reason, if she spends to much time with the captain she'll give a rightly hard slap.