Can you sue if you were fired based on verbal allegations but not actual physical proof?

Yes, you can still be fired. Your employer does not need "proof."

You may have claims against both. The claim against your employer would likely be workers comp.

Is it legal for my company to reprimand me over comments on an anonymous workplace survey?

This does not, in and of itself, seem illegal. Sorry.

Was there any illegal action ?

Impossible to say from the info provided whether or not there was illegal action.

A supervisor made multiple threats to destroy my mail. What is the legality of those threats and what are my options?

This sounds illegal and possibly criminal. So long as the mail is yours and not your employer's.

Is it illegal for my boss to not pay me for the hours I worked because he was not happy with what was accomplished?

what you describe is illegal. Consider contacting a lawyer who does FLSA or "wage and hour" work.

Wrongful Termination?

Your question is confusing. Did you take the drug test? Did you have the job? I am confused.

Can I sue a public University for GPA requirements for student government?

This does not really seem like illegal discrimination. Sorry.

I was fired for calling in sick w/o MD note 4 times after a last written warning, I am under treatment for insomnia, is this ok?

This may be a violation of the ADA and NY state human rights law for failure to accommodate. Call an employment lawyer.

Being blackballed or retaliated against.

unless it is bc of your age, race, gender, disability, etc., it is probably not illegal.