Is it permissible to fast and break fast based on the sighting in Saudi Arabia or Qatar, and is it obligatory to make up for last Tuesday?

The fundamental principle is that a Muslim relies on the sighting of the crescent moon in their own country for their fasting and breaking of the fast, provided that this reliance is based on a legitimate (Shar'i) sighting and not on astronomical calculations. If the official body responsible for crescent moon sighting does not adhere to Islamic legal standards, and people are unable to conduct their own sighting or announce a sighting, then it is necessary to fast and break the fast with the nearest country that observes the crescent moon in a legally sound manner. This aligns with the view of the majority of scholars that the sighting of the crescent moon in one country obligates all people to fast. Therefore, whoever fasts or breaks their fast based on the aforementioned is correct and does not owe any make-up fasts.