Is it obligatory for a Muslim to offer a sacrifice every year once he has offered it for the first time? And does he sin if he does not? And is it obligatory for him to make up for the sacrifices his father missed due to lack of financial ability?

The belief that performing Sunnah acts makes them obligatory for life is false. Performing a Sunnah act once does not make it obligatory, such as fasting six days of Shawwal or offering the Udhiyah (sacrifice). The Udhiyah is a confirmed Sunnah (Sunnah Mu'akkadah) and not obligatory according to the majority of scholars. It is almost as if there is a consensus among the Companions on this matter, and Abu Bakr and Umar abstained from it out of dislike for people to perceive it as obligatory. The shaykh's assertion that the Udhiyah is obligatory for his deceased father, who did not offer it due to his inability, is incorrect. The Udhiyah was not obligatory for the impoverished father, and therefore it is not obligatory for his son.