Is it permissible to open an account in a usurious bank (Housing Bank) for the purpose of receiving money transfers from siblings to cover the parents' expenses, and is dealing with this bank for this purpose only considered forbidden?

If your brothers can transfer the money through a non-riba-based bank, it is not permissible for them to transfer it through a riba-based bank. However, if they find no other means, then there is no harm in it. It is permissible for you to receive the funds and open a current account in a riba-based bank if there is unusual hardship, provided that you do not engage in other prohibited transactions. This is based on the permissibility of necessity, in accordance with the verse: "But whoever is compelled, without desiring it or exceeding due limits, then there is no sin upon him." This is also because hardship brings ease, and when a matter becomes difficult, it expands.