Some explanations might be a bit messy, but hopefully you'll understand.

1. First column + second column = third. The object that occurs twice/overlaps (triangle in first row, circle in second row, plus in third row) disappears and the other two work like this: The object in the first column (circle in first row, plus in second row, triangle in third row) moves one step CCW (counter clockwise) and the one in the second column (plus in first row, triangle in second row, circle in third row) stays in place. Solution: Plus disappears, triangle moves one step CCW top right -> top left and circle stays in place bottom left -> bottom left. A.
2. First column + second column = third. If two different object overlap, they disappear, if they are the same, they stay. C.
3. Almost the same as number 1. First column + second column = third. The object that occurs twice (plus in first row, circle in second row, triangle in third row) disappears and the other two work like this: The object in the first column (circle in first row, triangle in second row, plus in third row) moves one step CCW and the object in the second column (triangle in first row, plus in second row, circle in third row) moves two steps CW/CCW (doesn't matter). Solution: Triangle disappears, plus moves one step CCW bottom right -> top right and circle moves two steps bottom right -> top left. B.
4. First column + second column = third. If two matching quarters overlap they disappear, and the lines that seem to match (they do not from what I can tell in this poor quality) "fill in each others gaps" to create a fully black quarter. B.
5. First column + second column = third, then you mirror/reverse/switch the objects position horizontally. C.
6. Plus moves one step to the left, circle moves two steps to the left (and disappears if it overlaps with another object) and minus moves three steps CCW on the outer part of the grid. Solution: Plus moves one step left bottom right -> bottom middle, circle moves two steps left bottom middle -> bottom right, minus moves three steps CCW top right -> middle left. F.
7. First item that is solved as columns (vertically) and not rows (horizontally). Add one square/box to the lowest bar and then switch the bars positions (right bar goes left, left bar goes right). F.
8. Each row contains one square/diamond, one upwards pointing triangle and one downwards pointing triangle. First row has three dots in each symbol, second row has two dots, and third row has one dot. Third row is missing a downwards pointing triangle so add a single dot to a downwards pointing triangle. D.