Yes, there was no moon when Kaguya arrived on Earth. And for the Infinite Tsukuyomi to be activated, the presence of a moon is a primary condition.
So, in Naruto: Shippūden episode 460, Kaguya activates the Infinite Tsukuyomi. She does so by using her space time jutsu Yomotsu Hirasaka to open a portal and use a moon from somewhere else.
The animation of the ...
No. They were all of the same age. They were classmates. Kakashi was made the genin much earlier owing to his skills, whereas Obito and Rin joined him later. In episode 385 of Naruto Shippuden, Obito clearly mentioned "but he is the same age as we are" (from the past memories).