Is it permissible to take out a loan to perform the Hajj pilgrimage, given that the borrower is a resident of Saudi Arabia and will repay the loan immediately upon receiving his salary after Hajj, and he has a bank account in Egypt, but the transfer process might be delayed?

It is permissible for a person to perform Hajj with money belonging to someone else, but he is not obligated to accept it, and he does not become "capable" (mustati') by it, according to the preponderant opinion. Borrowing for Hajj is not disliked if the borrower is able to repay. However, begging and accompanying people for Hajj relying on their expenses are disliked.