So Mr. Sun, you want a detailed reply. During the first 15 years after independence, Dr. Rajendra Prasad and Dr. Radhakrishnan gave valuable advice and guidance to Mr. Nehru and his Cabinet. Not only that, these two great Presidents projected newly-independent India's image throughout the world. However, let us take the example of Fakruddin Ali Ahmed and Gyani Jail Singh. These two were real titular Presidents of Mrs. Indira Gandhi. They never botherd to raise their voice when emergency was declared (in 1975) and when anti-Sikh pogrom was going on (in 1984).
Now let us come to the power of the President as per the Constitution of India. Although the President exercises his/her power as per the advice of the Prime Minister, there are some situations when he/she has to take decision independently. As for example, if after the Lok Sabha election, no party/coalition gets clear majority, the President has to use his/her own discretion to call a party/leader to form Government. Secondly, a President can return a Bill or hold a Bill as per his own discretion. These two are very important aspects of Presidential power.
If a President can't take coherent decision due to his/her age or otherwise, should he/she be made President?
Non-violence is the greatest Dharma; So too is all righteous violence.