It is makruh to single out Saturday for fasting. If one fasts another day along with Saturday, then it is not makruh. For different scenarios for fasting on a Saturday, see the detailed answer.

If a person is observing an optional fast and something happens and he has to break his fast, then he should break his fast. You do not have to make up the day when you broke your fast, because the one who is observing an optional fast is in charge of himself.

Fasting on Mondays and Thursdays is recommended and is not obligatory. So, there is nothing wrong with fasting only on Mondays if one cannot fast both days.

It is not a necessary condition that the six days of Shawwal should be fasted consecutively. If you fast them separately or consecutively, it is OK.

Whoever fasts six days of Shawwal will have recorded for him a reward as if he had fasted a whole year. For more, please see the detailed answer.

1. The day of ‘Ashura is one of the significant days on which the Prophet (peace be upon him) prescribed we should fast. This day is not for Moosa (peace be upon him); rather it is for the saving of the believers. 2. The reason for fasting it is that it is the day on which Allah saved Moosa and drowned Pharaoh and his troops, and there covered them from the sea that which covered them. So the Prophet fasted on this day, and he enjoined the Sahaabah to fast on this day too. 3. When Allah enjoined fasting the month of Ramadan, this ruling was abrogated, and fasting on this day became Sunnah.