Is the use of artificial hair extensions (wigs) for styling hair at women's parties considered among the actions for which the doer is cursed, and is repentance for it permissible, and will Allah forgive this sin?

Joining hair with human hair or impure hair is impermissible. As for joining pure hair with non-human hair, there is a difference of opinion. Some scholars have permitted al-qaramel (silk or wool threads fashioned into braids that a woman attaches to her hair). However, the safer approach is to avoid this due to the general prohibitive evidence, such as the Prophet's (peace be upon him) absolute prohibition of hair extensions and his forbidding it even in cases of apparent need, for he "cursed those who connect hair." Furthermore, birthdays are not part of Islam, and it is not permissible to imitate disbelievers in celebrating them.