How can the zakat on a deceased person's wealth be calculated for the period from 1998 to 2018, and is it permissible for the children to pay it from their own money, given that his wealth decreased from $400,000 to $150,000 during this period?

As long as you are not certain that your father did not pay zakat (definition) for those years, zakat does not need to be paid from his estate after his death. The default assumption for a Muslim is that they are keen to fulfill what Allah has obligated upon them. Your father's consistent payment of zakat before his return to his country confirms his diligence in performing it, so there is no need to doubt him. If it were proven that he did not pay zakat, then it would be paid from his estate, not from the private wealth of his heirs. However, if some of his children voluntarily pay it from their own money, there is no harm upon them, and they will be rewarded, but it is not obligatory for them to do so.