Is it obligatory to offer the expiation of feeding sixty needy people for each day one intentionally broke their fast in Ramadan, and how can the number of unknown days be estimated, and is the feeding to take place in the country where the breaking of the fast occurred?

You are not required to make up the days of prayer and fasting that you missed before reaching puberty, because you are not held accountable before puberty. This is based on the Prophet's (peace be upon him) saying: "The pen has been lifted from three: from the child until he reaches puberty, from the sleeper until he awakens, and from the insane until he regains his sanity."

As for one who intentionally abandoned prayer and fasting after puberty, repentance is obligatory upon him, as is making up what he missed. He should estimate the amount that he believes will absolve his responsibility. No expiation is required other than making up the missed obligations, unless the abandonment of fasting was accompanied by sexual intercourse during the daytime in Ramadan after puberty. In that case, the severe expiation is required, which is fasting for two consecutive months for each day. If unable to do so, then feeding sixty poor people for each day.