How Old Does A Kitten Have To Be?

How old does a kitten have to be before it can go out in the house? I’ve been told that if they’re just under 10 weeks, they shouldn’t. But my cat was born May 3rd and she’s only eight weeks now….

Is there a certain age for when a kitten should be able to play by itself? My father has an 8 week old kitten and he will not stop playing with him. He climbs all over him, chases him around…