Can an employee be terminated on the grounds of speaking ill about co.

Yes. When the employment itself is on good faith, Employees are prohibited to talk bad about company as as to degrade its services. An Employee can be terminated on this ground as he/she committed breach of terms and conditions of appointment order.

Can't be done, but they can initiate disciplinary action after enquiry if the charges are proved, minor punishment can be imposed. Punishment depends on the post held by the delinquent officials. In any case punishment of dismissal or termination is disproportionate and therefore it can be challenged in the appropriate legal forum depending upon the post held by the delinquent official.