The crosshair isn't a static color, it should always be the inverse of whatever color is below the lines to ensure visibility, so there isn't a way to change the color as far as I am aware of.
You can turn off the crosshairs and use a regular mouse cursor instead by going to Tools -> Drawing Aids -> Toggle Crosshairs
No, but this request is on the wish list. The cross-hairs and other cursor items are drawn using what's called a exclusive-or (XOR) drawing mode. This mode works very well when there is a good contrast between opposing values in the color space (e.g. white and black or red and green), but poorly when there is poor contrast (e.g. grey to grey or pastels to pastels).
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You can turn off the crosshairs and use a regular mouse cursor instead by going to Tools -> Drawing Aids -> Toggle Crosshairs