How many years of prayer must be made up by someone who began praying at the age of 15? Should it be calculated from the age of 10 or from the age of puberty?

You are not required to make up any missed prayers except for those you missed after puberty. The pen is lifted from a child until he reaches puberty. The command to order a child to pray at seven and to hit him for it at ten is for his training, so he gets accustomed to it, not because it is obligatory upon him.