Is the age of 18 considered the correct age of accountability ( تكليف)? And what should someone who has been making up missed prayers based on this age do, if they had intended to continue making up missed prayers for life: should they abide by their vow or suffice with supererogatory prayers?

The intention to continue making up missed prayers is not considered a vow, and nothing consequential arises from it. It is sufficient to pray until it is highly probable that all missed prayers have been made up. If it is possible to accurately determine the number of missed prayers, then doing so is obligatory. This is done by calculating them from the age of puberty until the age of 34. The age of puberty is 15 years if one does not recall the time of ejaculation or the growth of coarse hair around the private parts; otherwise, the age of accountability begins with that if one remembers it.