Hi, I guess you still want to put the experience into your resume since working experience is very important for you to find another job. But make sure don't put any bad words about the firm into your resume. Doing that only can stop people call you for interviews. Yeah, I have been bad-mouth one time by my past employer and lost an offer. But not every new employer will trust everything what you past employer said. They will make their own judgments.
Don't hate me. But even I am your boss, I may let you go. Doing home work at office, napping, bad mouths the colleagues, there are a lot of things you did wrong. I can trust you that you didn't use the firm's time, but still it looks very bad.
Move on and don't let the bad things take you any more time. I don't think you need to take any legal actions too, it is kind of waste of time.