When people like and/or leave comments to my post, will this be displayed on my Facebook page?

No, it will not. The case is, Like for a WordPress site is a Like of a certain URL, but not the page content, while on Facebook it's Like of the content, not the URL. I.e. these are two different things, and it is impossible to link them.

For more data on the Like button, please check the developers' page.

 

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