Yes, you may bring your spouse and unmarried children under the age of 21 in the same visa category. They can stay as long as you maintain the status on the derivative I visa status.
You can apply for derivative status along with your I visa application. If your dependents apply for visas at a later date, a copy of your I visa must be furnished with the application.
No, your dependents may not work while on the dependent status. They have to apply for appropriate work visa.