12. (10 points) A piece of paper is flipped over, the numbers $0$, $1$, $8$ remain unchanged after a $180^{\circ}$ rotation, $6$ becomes $9$, $9$ becomes $6$, and other numbers have no meaning after a $180^{\circ}$ rotation. How many 7-digit numbers remain unchanged after a $180^{\circ}$ rotation? Among these, how many are divisible by 4? What is the sum of all 7-digit numbers that remain unchanged after a $180^{\circ}$ rotation?
【Analysis】According to the problem, the 7-digit number $\overline{\mathrm{ABCDEFG}}$, when rotated 180 degrees, remains unchanged, indicating that this 7-digit number is composed of $0, 1, 8$. We can list them accordingly, and then solve the problem based on the characteristics of numbers divisible by 4.

【Solution】Solution: (1) If the 7-digit number $\overline{\mathrm{ABCDEFG}}$ remains unchanged after a $180^{\circ}$ rotation, then $D$ must be one of $0, 1, 8$. $C$ and $E$, $B$ and $F$, $A$ and $G$, these three pairs of digits can only be $0, 1, 8$ simultaneously, or one 6 and one 9. Therefore, we only need to determine the four digits $A, B, C, D$. $A$ can be one of $1, 6, 8, 9$, 4 choices; $B$ can be one of $0, 1, 6, 8, 9$, 5 choices; $C$ can be one of $0, 1, 6, 8, 9$, 5 choices; $D$ can be chosen from $0, 1, 8$, 3 choices. Therefore, the total number of 7-digit numbers that remain unchanged after a $180^{\circ}$ rotation is $4 \times 5 \times 5 \times 3 = 300$ (numbers).
(2) Among these, the numbers divisible by 4 must have their last two digits as $00, 08, 16, 60, 68, 80, 88, 96$. Among these, the numbers ending in $00, 80, 60$ will have a leading zero after a $180^{\circ}$ rotation, which is a contradiction, so they are excluded.

Therefore, the numbers divisible by 4 are $5 \times 3 \times 5 = 75$ (numbers).
(3) The positions $A, G$ have $1, 8, 6, 9$ each appearing $5 \times 5 \times 3 = 75$ (times),
The positions $B, C, E, F$ have all digits appearing $4 \times 5 \times 3 = 60$ times, and the position $D$ has $0, 1, 8$ each appearing $4 \times 5 \times 5 = 100$ times,

Therefore, the total sum of all 7-digit numbers that remain unchanged after a $180^{\circ}$ rotation is:
$$
24 \times 75 \times 1000001 + 24 \times 60 \times 110110 + 9 \times 100 \times 1000 = 1959460200.
$$

Answer: There are 300 7-digit numbers that remain unchanged after a $180^{\circ}$ rotation, among which 75 are divisible by 4, and the total sum of these 7-digit numbers that remain unchanged after a $180^{\circ}$ rotation is 1959460200.

Therefore, the answers are: $300; 75; 1959460200$.