Is it permissible for a girl to accept a gift sent via shipping from her friend whom she considers like a brother? And is anything required of her if her nail breaks during Umrah?

Familiarity between young men and women, and what is known as love relationships, companionship, or friendship between them, is a gateway to evil and corruption. Claims of its innocence do not remove it from being a pretext for what is impermissible. Therefore, you must sever your relationship with this young man. It is not permissible for you to accept a gift from him to perpetuate this unlawful relationship. If you have already taken possession of the gift, you must dispose of it by spending it on charitable causes.

Regarding your fingernail breaking while you were in the state of ihram for Umrah, nothing is required of you for that.