What is the ruling on fasting Saturday alone to make up for the six days of Shawwal, and is it permissible to fast Saturdays and Sundays consecutively each week to complete the six days of Shawwal?

The correct view is that fasting on Saturday alone is reprehensible (makruh), not forbidden (haram). As for starting the six days of Shawwal fast on a Saturday, there is no harm in it, because the prohibition applies to singling out Saturday for fasting without fasting a day before or after it. Fasting on both Saturday and Sunday to complete the six days of Shawwal is permissible, as long as Saturday is not singled out for fasting alone.