Ask a landlord-tenant lawyer and get answers ASAP
Yes, if they have no authority to lease the premises to you then you can sue for breach of contract.
You can sue for breach and you may be able to sue for fraud. If you prevail on the fraud claim then you may be entitled to punitive damages and attorney fees, as well as your actual damages.
You will want to retain local counsel for this. If you need assistance finding local counsel try Martindale Hubble (site rules prohibit us from referring specific attorneys) . Many attorneys themselves use this site to locate attorneys outside their jurisdiction or expertise:
http://www.martindale.com/Find-Lawyers-and-Law-Firms.aspxIt is a huge worldwide database searchable by location and specialty. The attorneys are all peer rated. So, they represent the top of the profession.