Is it obligatory to make up for missed prayers for someone who abandoned them for many years due to ignorance and laziness, and how is this makeup performed, and is expiation due for that?

Prayer is not obligatory until one reaches puberty. Puberty is marked by the emission of semen with desire, or the growth of coarse hair around the private parts, or reaching the age of fifteen Hijri years. For females, menstruation is an additional sign. Prayer before puberty is not obligatory. As for the prayers the questioner missed since reaching puberty, there is no consensus on the obligation to make them up, although it is more prudent to do so. If one chooses to make them up, no other acts of worship, such as Hajj or Umrah (definition), can substitute for them. It is permissible to make up prayers in congregation with one's wife with the intention of making them up. It is possible to make up two days' worth of prayers with each day, and this is the view of the Malikis, and there is no harm in acting upon it.