Would a wife be unlawful to her husband if she swore – at his request – that she had not created a Facebook account, intending that she had not created it with her original email, while she had created it with another email?

A wife declaring her husband forbidden to her does not result in divorce or ẓihār. She is obligated to offer an expiation for a broken oath (kaffārat yamīn) if she breaks it, as stated by Ibn Nujaym al-Ḥanafī: "If she said to her husband: 'You are forbidden to me,' or 'I have forbidden you to myself,' then it is an oath, such that even if she accedes to intercourse with him, or if he forces her, she is obligated to offer the expiation."

If you intended something plausible and you are truthful in your intention, then there is no expiation upon you, because an oath is based on the intention of the one swearing it, unless he is unjust or the one administering the oath is a judge. This is supported by al-Nawawī's statement: "As for swearing an oath without the judge's administration, and one uses tawriya (ambiguous speech), the tawriya benefits him, and he does not break his oath, whether he swore it spontaneously without being prompted, or someone other than a judge or his deputy prompted him to swear it. The intention of the one administering the oath, if not a judge, is not taken into consideration." It is necessary to be cautious about returning to such an oath, as making the husband swear by divorce is wrong, and swearing by it is among the oaths of the dissolute. It may lead to severe consequences, for the lawful oath is by Allah Almighty.