Question

Did veer savarkar apologise to british government to stay out of jail

Answer 1

Savarkar sent two letters for clemency, first in 1911 and 1913. In a letter dated November 14, 1913 [1] by Savarkar  to Home Minister of India - 

Now no man having the good of India and Humanity at heart will blindly step on the thorny paths which in the excited and hopeless situation of India in 1906-1907 beguiled us from the path of peace and progress. Therefore if the government in their manifold beneficence and mercy release me, I for one cannot but be the staunchest advocate of constitutional progress and loyalty to the English government which is the foremost condition of that progress. As long as we are in jails there cannot be real happiness and joy in hundreds and thousands of homes of His Majesty's loyal subjects in India, for blood is thicker than water; but if we be released the people will instinctively raise a shout of joy and gratitude to the government, who knows how to forgive and correct, more than how to chastise and avenge. Moreover my conversion to the constitutional line would bring back all those misled young men in India and abroad who were once looking up to me as their guide. I am ready to serve the Government in any capacity they like, for as my conversion is conscientious so I hope my future conduct would be.

In 1920 Congress, Gandhi, Patel, and Tilak demanded for an unconditional release of Savarkar. He was released in 1921, but on a few conditions. He agreed to be restricted to Ratnagiri District of Maharashtra, and had to take permission from British for travelling outside. He renounced violence, and active nationalist politics. Police restrictions on his movement were lifted in 1937 after the grant of Provincial Autonomy.