First off, let me introduce myself...I have been a motorcycle technician/mechanic for pretty much most of my life which pretty much is approaching the 40 yr mark in the industry. Started out working on my own machines, got a job at a Kawasaki dealership that changed hands a couple of times, was there for 11.5 years then moved on to working for Kawasaki Motors Corporatin for 14 years.
So in my 11.5 yrs in the dealership ,we became the ZN1300 Voyager kings, we pretty much emptied Kawasaki's distribution warehouses and other dealer's inventories.
I became the so called Voyager king, a title given by my customers, dealership and Kawasaki.
It's been a VERY long time since I've seen or touched a Voyager and have forgotten a whole lot but will try to reach back into my memory banks to help steer you in the right direction.
So first things first, you said you replaced the starter relay, this part is located in the junction box. Did you try replacing the starter solenoid?? Over time the contacts wear and will stick together.
How many miles are on the bike??
The Voyager engine was notorius for loading up the spark plugs and valves with carbon soot do to its lower cruising RPM, alot of the time (believe it or not) giving the engine a few good quick static full throttle revs with the engine at normal operating temperature would clear the popping/chirping heard form the exhaust. Not to say that thats your problem, the other possible causes are numerous so I'll try to run through a few semi simple things.....Dripping or dirty injectors, Dripping may be caused by injector nozzle sleeves having workied their way slightly off (They CAN be pushed back on).
Intake leaks are also a culprit...In general all the intake leaks were solved by by sealing the intake manifold to the head with Threebond 1211, Sealing them was a common practice for me whether they needed it or not because they WOULD evenually leak. Make sure they are not cracked and or falling apart.
Make sure vaccuum hoses are in good condition.
Make sure the clean air valve is functioning properly if so equiped.
Tight valve lash can also contribute to exhaust popping/chirping and will also degrade engine performance and fuel consumption.
Throttle bodies being out of sync.
Make sure your air filter is in good clean condition.
As for your fuel gauge.....Numeous items are possible....Unplugged (Sending unit in tank), cut/damaged wiring, Bad sending unit, bad gauge in instrament cluster, bad fuse.or could possibly be a bad diode/diode block.
Check ALL fuses and connections before you condemn parts.
Good luck and let us know what you find.