How is Zakat calculated on money in a savings account from which funds are deposited and withdrawn, and must amounts that have not completed a full year be excluded when calculating Zakat, given the existence of a car loan and a home loan?

Saved money in an account is subject to zakat on whatever portion of it has completed a full year (hawl), provided it reaches the niṣāb or more. As for deposited amounts that have not completed their hawl, zakat is not due on them upon the completion of the hawl for the first amount of money. Its owner has the choice regarding the zakat of these amounts: either to expedite their zakat along with the first money (as a voluntary act), or to pay zakat on each new amount when its hawl is completed. The easier option is to pay zakat on all of it when a full year has passed on the first niṣāb you possessed.