7. (i) (Grade 11) Let $A=\{2,4,7,8,13,15\}$. If a non-empty set $M$ satisfies that adding 4 to each element of $M$ results in a subset of $A$, and subtracting 4 from each element of $M$ also results in a subset of $A$, then $M=$ $\qquad$
(ii) (Grade 12) Randomly fill the numbers $1,2, \cdots, 9$ into the nine cells of a $3 \times 3$ chessboard (one number per cell). The probability that the sum of the numbers in each row and each column is odd is $\qquad$
(ii) $\frac{1}{14}$.

In $1,2, \cdots, 9$, there are 5 odd numbers, which must occupy exactly one row and one column. There are 9 ways to choose any row and column, so $P=\frac{9 \times 5! \times 4!}{9!}=\frac{1}{14}$.

(ii) $\{11\}$.
$$
\begin{array}{l}
\text { Let } A_{1}=\{x \mid x=a-4, a \in A\} \\
=\{-2,0,3,4,9,11\}, \\
A_{2}=\{x \mid x=a+4, a \in A\} \\
=\{6,10,11,12,17,19\}, \\
M \subseteq A_{1} \cap A_{2}=\{11\} .
\end{array}
$$

Since $M$ is non-empty, $M=\{11\}$.