They're correct on the first one. Its easier to explain the converse of it.
Imagine you are flying into a headwind equal to your normal cruise speed - ground speed is zero - its only by going faster that you achieve any range at all.
In a tailwind, by going slower, you are getting more of a 'free lift' from the wind vector.
More technically, the best speed is the tangent of the drag curve that crosses the origin displaced left/right by the amount of tail/head-wind.
As for the second question - If the options you give are correct, I agree that you'll collide in 18 seconds, so (a) is your only option.