The standard formulae for these problems are:
For any constant k, and a set of variables X.
You should be able to answer all 4 questions using those.
An intuition is below if you want one:
The standard deviation measures the average distance from the mean of the set.
If you add a fixed number (2) to every point in the set:
Every number increases by 2
So, The mean increases by 2
So the distance between each number and the mean doesn't change
So the average distance to the mean doesn't change
So the std.Dev is the same
If you scale ever number by a factor (2)
Every number doubles
So, The mean doubles
The distance between each number and the mean doubles
So the average distance between each number and the mean doubles
So the std.dev has doubled