cost accountant sign on projected financial statements

YES. HE CAN SIGN. THERE IS NOT STATUTORY RULE FOR THE SAME.

Sure, Cost Accountant can certify financial statement other than Stipulated as per Income tax act and Companies Act.

CMAs are eligible to certify internal audit report under companies act, GST Audit report, Certification for customs, Certification and audit under SEBI, certifications under Companies Act, Etc... CMA s are also eligible to  audit under different sate co operative society act.  So the question doesn't arise and CMAs can definitely certify financial statement.