[color=blue][i][b]If best L/D speed is maintained, what happened to glide range when there is an increase in headwind/tailwind?[/b][/i][/color]

For a given airspeed/thrust,

(a) a headwind will reduce your groundspeed and the glide angle (as observed by someone on the ground) steepens a bit - range decreases

(b) a tailwind will increase your groundspeed and the glide angle (as observed by someone on the ground) flattens out a bit - range increases.

In each case (presuming smooth air) the performance measured against the air mass stays the same.

[color=blue][i][b]If best L/D speed is not maintained, what happened to glide range when there is an increase in headwind/tailwind?[/b][/i][/color]

That all depends on the speed variations. However, if you are maintaining a constant airspeed, the effect of wind will be similar to the previous situation.