What should I do about my lying and claiming to have performed the tawaf and sa'i in the Sacred Mosque during menstruation for 'Umrah? Is sincere repentance sufficient, or does it require a fidyah (expiatory payment)? And is it permissible to postpone the fidyah until money is available?

You must repent to Allah for lying and for entering the mosque while not in a state of purity. If she intended to perform 'Umrah, she remains in the state of ihram due to not completing the tawaf and sa'i. If she is unable to go and complete the 'Umrah, then she is considered to be in the ruling of one who is prevented (muhsar), and she exits ihram by sacrificing a hady. If she is unable to provide a hady, she fasts for ten days and then exits ihram. However, if she did not intend 'Umrah, but only pretended to do so, then the rulings of ihram do not apply to her, and she must repent for entering the mosque while menstruating.