I take the questions beginning with "Do ye not know" and "Know ye not" to be rhetorical with the meaning "Of course you know that you shall judge the world and angels":
1Co 6:2 Do ye not know that the saints shall judge the world? and if the world shall be judged by you, are ye unworthy to judge the smallest matters? 1Co 6:3 Know ye not that we shall judge angels? how much more things that pertain to this life?
Why might he expect them (or us) to understand that? How is that so obviously the case?
I have read commentary suggesting that it is spoken of here:
Mat 19:27 Then answered Peter and said unto him, Behold, we have forsaken all, and followed thee; what shall we have therefore? Mat 19:28 And Jesus said unto them, Verily I say unto you, That ye which have followed me, in the regeneration when the Son of man shall sit in the throne of his glory, ye also shall sit upon twelve thrones, judging the twelve tribes of Israel.
However, I see only 12 seats mentioned and only in reference to Israel.
What makes Paul see the saints judging the world and angels as an obvious matter?
KJV unless otherwise noted.
See related: In Daniel 7:22 is judgment "committed to" the saints or "rendered in favor of" them?