Ok, Danger may count range and line of fire from any robot or vehicle. Now, does she benefit from HID's improved targeting (ignores hindering), as she uses its line of fire?

She doesn't get anything but the location from the figure she's attacking through. None of his powers or abilities matter in the slightest.

This is why it's useful to quote the effect in question:

ISLAND DEFENSE SYSTEMS: When Danger has one action token, she can draw lines of fire and count squares for range from any square occupied by a friendly character with the Robot or Vehicle keyword.

That make it pretty clear that Dange is the one drawing the line of fire, so abilities that effect how the other character draws line of fire won't apply.