Can I know who’s viewing my timeline or how often it’s being viewed?

No, Facebook does not provide a functionality that enables you to track who is viewing your timeline, or parts of your timeline, such as your photos. Third party applications also cannot provide this functionality. Applications that claim to give you this ability will be removed from Facebook for violating policy. You can report applications that provide untrustworthy experiences.

No. Private messages only appear in your Inbox on Facebook. Learn more about what's on your timeline.

None of your information – your name, basic info, what you like, who your friends are, what they have liked, what they recommend – is shared with external sites you visit with a plugin. Because they have given Facebook this space on their sites, they do not receive or interact with the information that is contained or transmitted there. Similarly, no personal information about your actions is provided to advertisers on Facebook.com or on the other site.