With the new hints this has become much simpler. In fact, OP has (unintentionally?) changed the character of the puzzle. At least some solutions can be step-by-step (like a sudoku for want of a better simile) reconstructed from the hints.
For example number 8 (I'll only do one, so people still have a chance to earn the bounty by solving one of the others):
Let us assume that in each non rectangular area every convex corner not touching the boundary is actually occupied and see how far we can get:
8 . b b b b b b .
7 . b b b b b b .
6 W!. . . . . . .
5 w . . . . . . B!
4 w w w W!. B!b b
3 w w w w W!b b b
2 w w w w w B!b b
1 w w w w w W!. B!
a b c d e f g h
w: white piece or empty .: empty W! white piece
b: black piece or empty B! black piece
Because of the white pieces on f1 and e3 the black piece on f2 can only be a N. As this N attacks h1 the h3 and g4 squares must be empty. Similarly, f4 must also be a black N and g2 empty. On h1 there cannot be a R or Q because of the white piece on f1. Black Ns are used up leaving a K or a B. But if h1 were a K h2 would have to be a B (the K has to attack something, and that something must not attack him back) but that would leave the N on f2 unreachable. Therefore h1 is a B, f3 is empty and there is a black piece on b7.
8 . b b b b b b .
7 . B!b b b b b .
6 W!. . . . . . .
5 w . . . . . . B!
4 w w w W!. bN. b
3 w w w w W!. b .
2 w w w w w bN. b
1 w w w w w W!. bB
a b c d e f g h
Of the black pieces still available only a R can sit on b7 without attacking the white piece on a6. The only way of attacking the knight on f2 without also attacking f4 or h5 or h1 is a B on h4. As the only piece that can attack the Q is a N and the f2 N already attacks another piece h5 must be the Q. To close the cycle g7 must be the K and f8 the other R.
With the black chain complete we can remove the remaining black markers and also all the white ones that are attacked by black pieces:
8 . . . . . bR. .
7 . bR. . . . bK.
6 W!. . . . . . .
5 . . . . . . . bQ
4 w . w W!. bN. bB
3 w . w . W!. . .
2 w . w w . bN. .
1 w . w . w W!. bB
a b c d e f g h
The piece on a6 cannot attack b7 ruling out Q,B,K nor can it be a N because there is no suitable white target, so it must be a R. This R can only be attacked via the a6-f1 diagonal. As there is piece on f1 a Q or B between a6 and f1 would attack at least two pieces. Therefore f1 must be the B and the rest of the diagonal empty.
8 . . . . . bR. .
7 . bR. . . . bK.
6 wR. . . . . . .
5 . . . . . . . bQ
4 w . . W!. bN. bB
3 w . w . W!. . .
2 w . w w . bN. .
1 w . w . w wB. bB
a b c d e f g h
Of the squares left the only one where the Q doesn't attack two or more other pieces is c2. To shield the black Nf2 there must be another white piece on d2 which in turn forces a2,a4,c1,c3 to be empty.
8 . . . . . bR. .
7 . bR. . . . bK.
6 wR. . . . . . .
5 . . . . . . . bQ
4 . . . W!. bN. bB
3 w . . . W!. . .
2 . . wQW!. bN. .
1 w . . . w wB. bB
a b c d e f g h
Only one of the a1 and a3 squares can be occupied. Indeed, a3 would have to be a N and a1 a N or B. They cannot both be Ns and B on a1 could only be reached by a R on e1 which would also attack f1 and e3.
With only one more square useable in the a-file e1 must be occupied. This leaves a1 as the only possible square for the dark-squared B, d4 as the only place for the K and e3 as the only place for the remaining R. The Ns go to d2 and e1.
Fully reconstructed position:
8 . . . . . bR. .
7 . bR. . . . bK.
6 wR. . . . . . .
5 . . . . . . . bQ
4 . . . wK. bN. bB
3 . . . . wR. . .
2 . . wQwN. bN. .
1 wB. . . wNwB. bB
a b c d e f g h
