The issue isn't you or me calling him out, it's whether Twitter is acting as a platform or publisher by annotating the tweet. The document here alleges that they are like a publisher, and will lose vital protection. This has serious implications.
I would think so, yes. In that case I wouldn't be surprised if the comment section is removed, or the moderation team of Fox News more carefully sticks to platform principles. Honestly not sure.
Fox News will be wholly empowered by this. This EO is a reaction to attempts to fact-check the White House, and Fox News is in a different line of business.
If/When Twitter is classified as a publisher do you believe they will be able to comment on the validity of things they publish? Like, for instance, a newspaper would?