What are the limits of a relationship with a girl upon whom the Fatiha has been recited and everything agreed upon, but the marriage has not yet been registered? And is it permissible to have intercourse with her before registration to alleviate menstrual pain?

If the conditions for a marriage contract are met, including the offer and acceptance in the presence of two witnesses, then the contract is concluded, and the girl becomes your wife, and whatever is permissible for a husband with his wife becomes permissible for you with her, even if it has not been registered. The custom in some countries dictates that the husband does not consummate the marriage with his wife until after the wedding ceremony, due to the benefit or the prevention of harm it entails. As for mere agreement and the recitation of Al-Fatiha, they do not constitute a marriage contract.