Is it permissible to give an approximate estimate for the zakat on savings from past years, and is it permissible to give this zakat to a sister to cover part of the cost of a car she wishes to buy, knowing that she wanted to take the amount as a loan?

Whoever is obligated to pay Zakat and did not pay it on time must repent to Allah and pay it for all the delayed years. If they cannot accurately determine the exact amount of savings, they should exercise ijtihad (independent reasoning) and act upon their best judgment. If the sister is not poor and is financially capable, then it is not permissible to give her from Zakat.