In re: What an President can do, if he wishes. 

The extent of the powers of an Indian President have never been tested in the Courts.

Say a President dismisses a Prime Minister a few weeks or months after a general election & appoints anyone he likes as the Care-taker Prime Minister.

Q: What does the now former Prime Minister do?
A: Maybe go to the Supreme Court.

Q: Say the Supreme Court directs that the Prime Minister be reinstated but the President refuses to do so. Who is expected to execute the Supreme Court's order? 
A: Possibly the Military - most of the top officers of which would have been appointed by the party to which the President belonged.

Q: If the Military refuses to do so, what can the former Prime Minister do?
A: Try and remove the President.

Q: How is an Indian President removed?
A: Impeachment requiring 2/3rds majorities of a majority of members of both houses of Parliament sitting separately. Such numbers cannot usually be achieved without the party to which the President belonged. 
So even if the former Prime Minister manages to initiate impeachment, which too is difficult, it would be most likely to fail.

Q: What next? 
A: I leave it to your imagination.