I am sorry. The monomial $x_1^a\dots x_6^f$ with $10=a+ \dots f$. In above fomular, $x$ means $x_i$.

Yes. Let $Sq^j$ be a square operation in Steenrod algebra. We have $$Sq^j(x)=\left\{\begin{matrix} x, \ \ \ \text{if $j=0$,}\\ x^2, \ \ \ \text{if $j=1$,}\\ 0. \ \ \ \text{otherwise.} \end{matrix}\right.$$ And it satisfies the Cartan fomular $$Sq^{n}(fg)=\sum_{i=0}^nSq^i(f)Sq^{n-i}(g).$$