It looks like someone tried installing a modern solid state regulator/rectifier unit , that makes the rectifier unnecessary.
The original regulators were bad and usually overcharge.
On my 75 Z1 (same harness as 76 KZ900) the four connections on the side of the battery case are brown (with a plug for wires to the front), white (where the rectifier plugs in), green (for the regulator) and blue for the alternator and engine sensors.
In your case it looks like the white plug not connected is the now unneeded rectifier, that can be removed.
For some reason it looks like they plugged the new regulator into the white connector and then left the old regulator still plugged into the green socket.
I believe the old rectifier and regulator should both be removed and the new regulator/rectifier plugged into the green socket with its white connecting to the white wire from battery and the fuse.
Does this charge ok?
Z1 Enterprises explains how to connect a new regulator/rectifier here.
Regulator Rectifier - Black - Z1 | Kawasaki and Suzuki Motorcycle Parts | Z1 Enterprises
I also attached a pic below of my Z1 connections with a new regulator/rectifier which I believe is correct.
As for the other issues, they may just be a matter of cleaning and tightening connectors. But to trace it down there's a nice color wiring diagram right here on this forum.
kzrider.com/forum/4-electrical/616057-z1...iring-diagram#850111
Good Luck,
Kurt