Spy Planes
The FBI has the power and technology to spy on you in your home. Obviously, they're not going to do that unless they really need to, but the option is always there. They are able to survey the perimeter of your home and watch who enters and who leaves the home. They also have infrared light cameras which can monitor what is going on inside. Just like any type of surveillance, they need a warrant to do this.
They Can Speak Freely... Usually
Most people assume that FBI agents have to be tight-lipped, but that's not always the case. They don't always have to be super secretive about their jobs or positions within the department. They're usually free to talk about nearly any investigation they've been a part of as long as the case is closed. Open cases cannot be discussed, but that's pretty straightforward with anything that involves a criminal case.