what is the expectation of minimum order statistics? I want the expectation of minimum order statistics
and  the variance of minimum order statistics


The short answer is it depends.  Wikipedia has a great page on order statistics, https://en.wikipedia.org/wiki/Order_statistic.  Here is a brief summary.  We can start with
$$P[X_{(1)}> x]=P[X_1\cap X_2\cap ...\cap X_n> x]=[1-F_X(x)]^n$$
where $F_X(x)\equiv P[X\le x]$ so that
$$F_{X_{(1)}}(x)\equiv P[X_{(1)}\le x]=1-P[X_{(1)}> x]=1-[1-F_X(x)]^n.$$
We can then use the characteristic or moment generating function to identify or approximate the distribution of $X_{(1)}$ to ultimately determine its mean and variance.
For a continuous random variable $X_i$ the probability integral transformation yields $U_i=F_X(X_i)\sim \text{Uniform}(0,1)$ and $U_{(i)}=F_X(X_{(i)})\sim \text{Beta}(i,n+1-i)$.  Applying the inverse CDF function to a $\text{Beta}(i,n+1-i)$ random variable, $F^{-1}_X(U_{(i)})$, produces the random variable $X_{(i)}$.
