Is it permissible to celebrate birthdays by preparing cakes, juices, and the like? And is it correct to leave the place and not participate with family in these celebrations?

It is impermissible to celebrate birthdays or give gifts on such occasions, as it involves imitating the enemies of Allah. Imitation occurs simply by the resemblance taking place, even without the intention to imitate. One must advise family members gently and strive not to participate in the celebration, unless a greater harm would result from non-participation, in which case one may attend while disapproving in their heart. However, if the occasion is meant to mark reaching puberty and the end of childhood without intending to celebrate a birthday, then there is no objection to that.