Solution: (1) From the table, we know that the middle number is A, the upper number is a- 12, the lower number is a+ 12, the left one is a-2, and the right one is a+2.

a+(a-2)+(a+2)+(a- 12)+(a+ 12)= 5a；

(2)5a=2020，

a=404，

This is impossible, because a should be an odd number;

(3)5a=365，

a=73，

And because 73÷ 12=6. 1, 73 is in the first column of the seventh row.

Because we set a as the number in the middle of the cross box, it is impossible.