Do I enter my fuel expenses for the whole year even if my self-employment was only a few months? Is Turbo Tax making the calculation of the percentage for me?

Only enter your expenses for the time you were self-employed. TurboTax will make a percentage calculation based on the KMs you enter. You should have a log or records of how many KMs you drove in total during this period, and how many were used for self-employment purposes.