Your doing great so far. #6&7 are correct. For number 8, it is usually Karen and I instead of me and Karen.
The sentence with #9 & 10 would make more sense if it went “on Saturday, us and them ...”
#11 would become we so that the words “Karen and i” don’t become repetitive.
#12 is correct
#13 becomes us.
#14 becomes We
and lastly #15 become us.
I hope this helps:)