Swapping district in completed city
No.

This is answered in the rules in the description of the Diplomat:

You may not exchange the Keep district, any 
districts in the Bishop’s city, or any districts in a 
completed city of eight districts (seven with the 
Bell Tower in play). 
Note: If you are using the 
Diplomat in your game, you must remove the 
Cemetery from the deck since both cannot be 
used together.

It is verified in the FAQ:

Q: Can the Diplomat exchange one of his districts for 
a district from a completed city of eight districts?
A: No