jpsb asked:
"Question, what happens if K is seated after the court is in session? say Oct 5th instead of Oct 1st?"
I'm no expert, but seems to me that...
Any cases heard between Oct 1-4 will be decided by the eight Justices seated.
As of Oct. 5th, the "9th seat vacancy" is filled, and cases head after that will be decided by 9 Justices (Kavanaugh included).