My thought process for each:
7. In each row and column of the circles, the little square is on the inside of two circles and outside of one, and a single square is bolded. Going by that thinking, my best guess for an answer would a circle with an un-bolded square on the outside.
8. The rectangle on the far left has 4 sides and three lines. Each line intersects two sides. The square in the middle has 4 sides and 4 lines, but one of them only intersects one side. The triangle on the right has 3 sides and 2 lines, and both of them intersect two sides. If the number of sides minus one equals the number of lines (maybe the 4th line for the square doesn't count because it doesn't intersect two sides?), then the answer would be a shape that follows the same pattern. Maybe the bolded circle is the answer? It has no sides, so it doesn't have any lines. Also, the fact that it's bold makes a pattern with the other shapes (no bold rectangle, bold square, no bold triangle, bold circle).
11. This one is really tough. The only thing I can figure out is that each row and column has a group with 3, 4, and 5 lines. If that's correct, the answer should have 5 lines. The only problem is that multiple answers have 5 lines. I wonder what the size of each line signifies?
15. The ONLY thing I can come up with is that there is a +7 -7 pattern twice (1 8 1 and 7 0 7 0). But if that was the pattern, there wouldn't be a random 4 in the middle. I just don't know. I'm sure the answer is obvious, though. My guess would be -1.