number of "secret police" organizations in our own world. They keep the population in a state of fear here's a nice quote that highlights the Seekers power as well as the entitlement of the Nobility...

WH
Questions of Treason

"How . . . ? How can I renew our friendship?" It had never been friendship anyway, merely acquaintance, but it was too late to say that now. "You tell me she's been raised to the Blood. Any overture must come from her." Fear emboldened her. And panicked her as it had at Falme. "Why do you need me to be your Listener? You can take her for questioning any time you decide to." She bit the inside of her cheek to still her tongue. Light, she wanted nothing less than she wanted him to do that. Seekers were the secret hand of the Empress, might she live forever; in the Empress's name, he could put even Suroth to the question, or Tuon herself. True, he would die horribly if it turned out he had been in error, but the risk was small with Egeanin. She was only of the low Blood. If he put Egeanin to the question. . . .

Note that Bethamin can't even speak to Egeanin unless Egeanin initiates the conversation, also note that the Seeker doesn't need anything more than suspicion to put Egeanin (or even Tuon!) to the question, sure if he's wrong he'll probably die, but that doesn't change what happened to the person put to the questions. And from other areas in the book we know that it's unlikely a Seeker (or any Questioner) would be so clumsy as to not get a confession out of their subject!

As for Bethamin's fears... certainly she terrified of becoming damane ... the biggest abuse of power of the Empire

WH
Questions of Treason

He ordered her to pour him a cup anyway, and she obeyed hurriedly. She wanted to keep him talking, anything to delay the inevitable. She knew for a fact that Egeanin had not been killing sul'dam, yet her proof would condemn her to share Renna and Seta's sour fate. If she was lucky. If this Seeker saw his duty to the Empire as Suroth had. He peered into the pewter cup, swirling the dark apple brandy while she took her seat again.

But if you were reading the damn books, you'd note that she still has some hope that she would be covered up just like Renna and Seta.

Egeanin has even more to say...

WH
A Matter of Property

"Seekers do no need proof," she said, mocking his accent. "Seekers do find proof, and the finding do be painful."

Or there's Mat's assessment

WH
Pink Ribbons

They had people called Seekers, too, and from the little he had heard—even people who spoke freely about the Deathwatch Guard locked their teeth when it came to the Seekers—from the little he had heard, Seekers made Whitecloak Questioners look like boys tormenting flies, nasty but hardly anything to worry a man.

Go re-read the chapters I've quoted ... it's pretty clear.

Here's another quote on the Entitlement issue:

WH
An Unexpected Encounter

"You don't understand, Mat," Beslan said fiercely. "Mother still sits on the throne, and Suroth says she will rule all of Altara, not just what we hold around Ebou Dar, and maybe more besides, but mother had to lie down on her face and swear fealty to some woman on the other side of the Aryth Ocean. Suroth says I should marry one of their Blood and shave the sides of my head, and mother is listening to her. Suroth might pretend they are equals, but she has to listen when Suroth speaks. No matter what Suroth says, Ebou Dar isn't really ours anymore, and the rest won't be either. Maybe we can't push them out by force of arms, but we can make the country too hot to hold them. The Whitecloaks found out. Ask them what they mean by 'the Altaran Noon.' "

or how's this for abuse of power?

WH
An Unexpected Encounter

Suroth was living there, and the cooks had been outdoing themselves since she had had the lot of them flogged after her first meal.

There are dozens of little quotes throughout the series showing the casual brutality of the Seanchan Nobles.