Is it permissible to borrow money from a sister to send one's mother for Umrah, knowing that the sister does not require immediate repayment but there is an agreement to take the computer in the event of the borrower's death? And is it permissible to perform Umrah with a passport that requires a photo without a hijab?

It is permissible for the sister to help her mother with the 'Umrah (definition) if she is able to repay the loan. However, she should not travel without a mahram (definition) or trustworthy company. She may go to Medina with the intention of praying in the Prophet's Mosque and visiting the Prophet, peace be upon him, and supplicating for whatever she wishes. As for the loan agreement stipulating that her sister would take the computer in case of her death, it is invalid because a mortgage becomes void upon the death of the mortgagor or their bankruptcy before the mortgagee takes possession of the mortgage, according to the Maliki school. According to the Hanafi, Shafi'i, and some Hanbali schools, a mortgage is not valid unless possession is taken. It is not permissible to issue a passport for 'Umrah with an uncovered head and hair. Just as it is not permissible to travel without a mahram, it is not permissible to commit this sin for the sake of 'Umrah. If traveling with such a passport entails displaying the picture to those who are not permitted to see it, then the Hajj or 'Umrah becomes impermissible.