What is obligatory upon me and my father regarding delayed Zakat, and is Zakat due on my deceased mother, given that my father and mother used to pay Zakat annually in Ramadan for the previous year's balance, and my father does not recall if he paid Zakat for my personal funds that he deposited into my account, with my fear that I lacked the proper intention at that time?

Your parents made a mistake by delaying the Zakat, as it must be given at its due time; it is permissible to pay it in advance but not to delay it. They must know the time when the wealth reaches the nisab and pay the Zakat after a full year has passed over it.

As for the questioner, as long as he is certain that the Zakat was not paid for him, and he is doubtful whether his father paid it on his behalf, then he must pay it for all the past years because it is a debt upon him. If the father paid the Zakat on his behalf without his intention, it is not considered valid according to most scholars. However, some scholars, like Ibn 'Uthaymeen, consider it valid. There is no harm in adopting this view if he is certain that it was paid. But with doubt, it is obligatory to pay it.