They don't. In fact, as a response to the "fake news" hysteria, they've gone to a completely centralized "Trending News" bar, so it's identical across the country. [0] This is after they got in trouble last year for intentionally stopping the propagation of stories that painted conservatives positively. [1]

[0] https://newsroom.fb.com/news/2017/01/continuing-our-updates-... [1] https://gizmodo.com/former-facebook-workers-we-routinely-sup...

You may find this graphical representation of the differences between facebook news feeds interesting if you have not already seen it.

http://graphics.wsj.com/blue-feed-red-feed/

I don't think so. I had to purposefully subscribe to far right news sources and block a lot of mainstream media outlets in order to see much right-wing news in my Facebook feed. That trending news feed is still biased left though, I can't change that.