Is walking 11 kilometers to the Prophet's Mosque to perform Friday Prayer considered an act of extremism or rigor, and does it fall within the scope of the noble Hadith which mentions the great reward for one who "washed and bathed, arrived early, walked and did not ride, and drew near to the Imam"? And does the Prophet's Mosque have an additional reward compared to other mosques?

There is no harm for the questioner in traveling to the Haram (definition) from a distant place if no harm results from it. This is not considered extremism, and it is hoped that Allah will reward him for it. The Sunnah (definition) indicates the permissibility of coming to the mosque from a distant place seeking reward, as did Ubayy ibn Ka'b (may Allah be pleased with him). And as the Prophet (peace and blessings be upon him) indicated to Banu Salama when they wanted to move closer to the mosque, that Allah would record the reward of their footsteps for them.