Employment Law Questions? Ask an Employment Lawyer.
First, you'd have a case for your unemployment because they have to prove that you were terminated for misconduct. Just being terminated is not enough to block unemployment and without some greater basis for a termination (like drug use), they would have to have documentation and evidence to actually support a termination. So you will win that unemployment appeal.
Second, you should look at filing a claim against them for defamation of character given their treatment of you, by alleging a basis for termination when there is not one. You'll have to find a local attorney to file that claim.
As for any other type of claim, without a contract of employment making your termination only legal with "cause" they can technically terminate you without good cause rather than just lay you off. Their reason is bad, but it doesn't make the termination itself wrongful.
I would certainly report the employer to your state's department of labor, because asking you to work for free is clearly a wage and hour violation. While that doesn't give you a lawsuit (because you didn't actually work the hours), it could result in an investigation against and fine of the employer.