I don't believe actively sending false claims of copyright infringement can be called 'civil' still. It's going for the offense, instead of passively resisting.
Not necessarily. The Constitution requires that all people get equal enforcement of the law. If you can demonstrate that the perjury components are never enforced against companies, you can argue that perjury charges would be unconstitutional selective enforcement.
I wouldn't want to be one of the people who have to prove that, though.
https://en.m.wikipedia.org/wiki/Civil_disobedience