Is one sinful for delaying the treatment of large kidney stones that require traveling abroad for treatment? And what is incumbent upon him in terms of making up (fasts) or expiation if he was unable to fast Ramadan for years due to illness?

There is no sin upon you for delaying treatment due to lack of trust in medicine. Treatment is permissible or commendable and may become obligatory if its abandonment leads to perishing. As long as your illness is hoped to be cured, you are obliged to make up the missed fasts (qada'), not to offer expiation (kaffarah). Expiation is for those whose illness is not hoped to be cured and who are unable to fast because of it. This is agreed upon by the Hanafis, Shafi'is, and Hanbalis, and it is the less preferred view among the Malikis. However, the well-known view among the Malikis is that there is no expiation (fidyah) upon him.