Is it possible to integrate or use information of some other web application on your website ? on Real Time?

According to my title, Is it possible to integrate or use information of some other web application on your website ? on Real Time?

For Example#1: I have a Facebook page and I post daily. Is it possible that I integrate it to my website? Not my whole Facebook page but only post part (post component). Means view that part of a Facebook page on my website. Or can I use that Facebook post DATA on my website.

Example#2: If example#1 is not possible? So I'm keeping it more simple that can we use DATA of some other web application on our website? Means If it is updated on that web application so automatic it should updated on our website also (on Real time).

How it can be done through API? If that web application is providing? what if not providing? Or any other solution?