Is the Egyptian Saudi Finance Bank considered an Islamic bank, and is it permissible to take and benefit from its profits, or is it a usurious bank that one should not deal with?

We have no knowledge of the reality of the aforementioned bank, and it is most likely a riba-based (usurious) bank. Dealing with it involves two possibilities:

First: The bank invests funds in legitimate ways and specifies to the clients a percentage of the expected profits. This is a permissible and lawful Mudarabah (profit-sharing partnership).

Second: The bank invests in usurious loans or deposits, or if the interest is determined from the client's capital, not from the profits. This is a usurious loan and is forbidden.

For a Mudarabah to be valid, the loss must be borne by the capital owner, not by the agent (the bank), unless the agent has been negligent.