What can I do if Im being harassed by my girlfriends ex husband.

Contact an attorney and discuss the possibility of a restraining order.

A restraining order comes to mind but she is your sister. If you are serious contact an attorney and discuss the matter.

Damage due to lible/slander by a former employer

You did not ask a question.

Do I Have a case of a false police report?

Dismissal of criminal charges cannot generally be used as the basis for a civil suit.

Should i file a complaint with the insurance dept, or do you have any suggestion?

Lodge a complaint. If things do not turn out to your satisfaction, contact an attorney and discuss the matter.

Were any rights/laws violated??

None by your description come to mind.

Can i sue for slander/defamation of character?

Truth is a complete dense to slander. Issues arise as to whose truth would be believed. Difficult to collect evidence for criminal charges with the...

Can the other party get a harassment restraining order against my daughter/ can we get one against her?

Difficult to say. More hard factual evidence would seem to be in order.

I was offered employment, then it was rescinded due to inaccurate background check. Is this defamation of character?

Any civil remedy appears to arise from the laws of negligence.

How much jail tme for criminal threat

It can be a misdemeanor or a felony; the former can carry a year in jail and the latter, 2-3 years in prison.