Answer:
(Fatwa: 1209/918/H=1431)
(1) It is alright.
(2) She should either accept it or forgive and inform him, one of them is necessary.
(3) She would be sinful.
(4) Mahr is a debt, and when the debt is in cash, the rise and fall of its value will not be considered at the time of payment, rather it is wajib to pay only the amount which was agreed upon. It is not lawful to demand extra amount. Yes, if husband gives extra on his own willingly and without pressure and there is no evil in it, there is no harm in it according to Shariah.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband
