What is the benefit of fasting Shawwal?

Fasting six days of Shawwal after the obligatory fast of Ramadan is Sunnah Mustahab, not wajib. The important benefits of fasting six days of Shawwal is that is makes up for any shortfall in a person's obligatory Ramadan fasts, because no one is free of shortcomings or sins that have a negative effect on his fasting.

Should fasting in Shawwal be consecutive?

According to them, one may fast any of the six days of Shawwal. Neither do they consider it necessary for a person to fast the six days consecutively. So long as one has fasted six days either consecutively or separately, he has fulfilled the requirement and he will receive the same rewards.