Is it permissible to fast make-up and vowed fasts in the month of Shawwal, or is this month designated only for fasting the six days of Shawwal?

The six days of Shawwal are not called "the white six." Fasting vows and making up missed Ramadan fasts in Shawwal are permissible, as Shawwal is like any other month in which this is valid. The virtue of fasting six days of Shawwal is specific to it, due to the Prophet's (peace be upon him) saying: "Whoever fasts Ramadan then follows it with six days from Shawwal, it is as if he has fasted for a lifetime." There is no requirement for continuity in making up Ramadan fasts, and they must be made up before the beginning of the next Ramadan. As for fasting vows, continuity is required if the one who made the vow specified consecutive days; otherwise, it is not.