Chronology and targeted audience
I'm searching for a science fiction anthology aimed at the children's or YA market. It can't have been released any later than around 2002, since that's when I read it in my local (UK) library; but it may well be older.
The story I remember most vividly is about a girl who is either born on the moon or in space (I can't remember which), who is the first human to be born off-planet. It turns out that she has special abilities: specifically, there is a scene near the end where she addresses the UN or some other conference of world leaders, and they all applaud her. After, it turns out that no one was wearing a translator; the delegates are all convinced that she spoke their particular language, with perfect fluency. Her father is also somehow involved in the story I think.
Another story is about an Earth which has been invaded by aliens. Everyone is possibly dead except for one man who lives in the sewers, occasionally venturing out to steal food from the supermarkets, at great risk because alien patrols are everywhere. He has recurring nightmares about being chased through the sewers by the aliens, who have finally figured out where he lives; this may also involve his legs becoming paralysed at a crucial moment. At the end, this nightmare becomes a reality.
I believe there is also a story involving a kid picking up a mysterious phone call, and aliens are involved, but I'm much less sure of this one.
I think there was also a story involving some kind of spider creature or other weird alien, who lives in a kid's room and can communicate with him. Again, I'm less certain of this one.
I can't remember what the cover looked like, but I believe the interior had at least a few black and white illustrations.
There may also have been a black and white illustration of spider creature from story #4 inside the kid's room.