Facebook is testing a new feature that prompts users to “continue watching” videos that they’ve seen in News Feed, but never finished. The feature is a test, according to a company spokesperson, and appears at the top of some users’ News Feeds, but only on Facebook’s web version. This test is in its “early stages,” and as with all Facebook tests, it’s possible that the “continue watching” feature may never make it to all users.
Video moving to the side when you scroll is the new feature* of Facebook. You can't do anything about this, but you can send your Feedback to Facebook.
Instead clicking on video, hover over mouse on video, options will appear, click on pause button at bottom left side to pause video or on X mark at upper right corner to close it.
*For some countries this feature has been introduced a year back.