Is working for a financial brokerage firm that deals in trading, bonds, contracts, and stocks unlawful, given that the proposed position (Operations Manager) is not directly related to trading?

It is permissible to work in brokerage firms if they do not directly engage in or intentionally assist in anything prohibited. As for working in usurious banks, it is not permissible, even if your work is not directly connected to usury; this is because the core activity of such banks is prohibited. This differs from companies whose core activity is permissible, but in which something prohibited may incidentally occur. In such cases, it is permissible to work for them, provided that one does not directly engage in the prohibited act.