How Naruto can be a jinchuuriki if his mother is still alive? Inside the Infinite Tsukuyomi world, Naruto's parents are still alive, but Naruto is still a jinchuuriki. How is that even possible?

Even for an Uzumaki, extraction means death, so why would Minato transfer the Nine Tails to their son?
Can someone explain what's going on here?
What you need to remember is that the Infinite Tsukuyomi and Limited Tsukuyomi are very advanced illusions trapping people in a dream world where everything is possible and it is designed to make them happy. One of Naruto's dreams is to have his parent's with him so while in this illusion it does not matter that in reality his mother would be killed by the removal of the tailed beast because the illusion would prevent that from happening.

Remember it is just an illusion designed to trap the victim with their own happiness.