What happens to Variance when every observation is squared? What is the effect on the Variance of a set of observations if every observation in the set is squared?

In general, it’s impossible to say.
Consider the difference between the data sets $\{-1,1\}$ and $\{1, 3\}$, which have equal variances. When you square the values in the first one, the variance decreases to zero. When you square the variances in the second one, the variance increases.
