A dataset has skewness = 1 with missing data. Standard deviation around median is 1.5. How much data will be unaffected? There is no other description about the data, if it is univariate, bivariate, etc. neither the type of distribution is given.

I recently came across this question, I would like to know how skewness affects unaffected data percentage
This is not answerable in general. You don't even know the skewness or standard deviation around the median without missing data, so you can't compare those quantities. Without more information about the distribution there is no way to figure out how much data is missing, or where in the distribution the missing data is located.