Friending Men On Facebook?

As a new author I have a profile and page for myself to gain/meet new readers and enjoy the company of romance readers like myself. Thanks to author Marie Force's awesome blog I have been friend-ing people like crazy but I hesitate to friend men.
I want to ask fellow female authors and female readers: do you friend men who are not directly related to you or know in real life?

The few men I have friend-ed immediately message me. They come from all parts of the world and want to chat, almost always asking me to turn on my camera.
Red Flag #1? Or am I just a paranoid?

What happened to facebook? I have nothing on my profile that suggests I am offering anything but me as an author. My picture is only of my face and shows nothing else, so what is happening here?

Is there a creep filter I can enable?