When I was a kid, I had an anthology of sf stories, and now I'm trying to see if I can recover/rediscover any of them. The book itself was a hardback. I read this as a kid, so some time in the 90s. But it's quite probable the book itself was quite a bit older (maybe from the 70s or 60s).
Here are the stories I more or less remember:
In a world where most people have become smaller to combat overpopulation/crowding, 2 siblings live in a cave with their father. One of them has a stuffed teddy bear. For some reason, they have to go into the city (where all the small people live, maybe to get food?) They're able to use the small vehicles and tools, since they're not full-sized adults themselves. But they are captured and eventually sent off-world as slave labor to some other planet. Once on this planet, they're rescued by the local aliens, who closely resemble the stuffed teddy bear. This might be the same story as posted in this question.
Two linked stories about a boy (possibly from Texas) who has 2 different encounters with aliens. In the first, 1 alien ship shoots down another. When they're both on the ground, they proceed to argue and threaten each other until the boy intercedes and convinces them to become friends. Ultimately, the 2 aliens leave together in the undamaged ship (the "passenger" alien makes some sort of comment that his crashed ship was insured). In the other story, the boy again encounters aliens, this time a delegation to welcome earth to some sort of galactic federation. The boy feeds them some really spicy chili, at which point the aliens think the kid is trying to poison them and fly off, which of course means the earth is no longer able to join this galactic federation.
In another story, a boy visits his uncle (I believe it's his uncle), who has a time machine. The boy activates it (I believe accidentally) and goes to a time of cave men. To ward them off, he builds a fire and sticks a sharpened stick into it to harden it into a spear. After he returns to his own time, the cave men repeat the process of fire-hardening the wood stick, and it turns out the boy inadvertently led to man's invention of tools.
In another story, a space ship is traveling (to some distant star, maybe?) A boy is in charge of navigation, and makes some sort of miscalculation which ends up causing the ship to go off course, and be stuck wandering outer space forever.
Another story has a child (maybe 2 children?) who happily live in an alien world—their parents came from an extremely polluted earth, but the kids don't miss it because they've grown up on this new planet. At some point, the parents decide to go back to earth with their kids, which makes the kids angry.
I'm pretty sure there are other stories in the anthology, but I don't want to misremember and provide false details.