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 theaverage distancefrom 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