Answer:
no relation
Mahatma gandhi can be said as the god father of indira gandhi.
Not at all. There was no blood relation.
There is no direct relationship. Indira Gandhi was married to Feroze Gandhi, no relation to Mohandas (Mahatma) Gandhi.
Indira took the name of Gandhi when she married Feroze Gandhi, who was not related to Mahatma Gandhi either (although Wikipedia claims Mahatma Gandhi adopted Feroze so he could marry Indira, but another source says he was persuaded--not adopted--by Mahatma to change his surname).
However, Indira was the daughter of another prominent political leader of 20th century India, Jawaharlal Nehru (1889-1964), the first prime minister of India and a protege of Mohandas Gandhi.