Can sponsor call police and U.S Ambassador to investigate or expel me

Your financial sponsor can threaten you with rack and ruin, but as long as you are able to maintain your F-1 status and exhibit sufficient financial support without illegally working in the country, you would likely be immune from her threats. I do note that if your cousin makes the complaint to the embassy and you later return to obtain another visa, you may be questioned on her allegations if there is a record made of her complaint.Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.  

As long as you are still enrolled in school, there is no legal basis for you to have to return to your home country.   The threat to have you deported is an empty threat.