Is it permissible for me to marry a man who will divorce his wife - who is my sister's friend - knowing that he works in a bank and wishes to change his job, and is diligent in performing prayers in the mosque?

Mixing between men and women is forbidden, and one must repent from it. It is forbidden for a woman to seek the divorce of her Muslim sister, and it is not permissible to incite or tempt a husband to divorce his wife. If the desire for marriage comes from the husband without you seeking to separate him from his wife, then it is permissible for you to accept, but it is not recommended for the following reasons: he might become attracted to someone else just as he did with his wife, and this will stir up animosity and hatred in his wife's heart, and his work in the bank might prevent him from leaving it. If, after deliberation, you decide to accept marriage from him, then seek Allah's guidance (perform Istikhara) and wait until he switches to another permissible job.