Don't know how to check the timting on my ZRX

Check this out. page 1-9.
Kawasaki zrx 1100 zr 1100 Service manual Download service repair owner...

Also, Fuel system is at section 2.
2-2 has a detail of the carburator.

When the chain adjusters are nearing maximum adjustment range the chain is definitely ready to be replaced. Rapid stretching is not a good sign. It is good that you are concerned about the condition of the sprockets. Most guys don't even think a sprocket wearing out. Below is a diagram showing different wear patterns on sprockets.

Check all your fuel lines, make sure that they haven't perished. Also check all your fuel hose connectors make sure they are tight not constricting. If you have to tighten your hose clamps so tight that the pipe bulges, then your fuel hose is junk. If you only have those spring clips, get rid of them and put decent hose clamps on.
Take off your seat, and locate the breather pipe at the back of your tank. Make sure that this pipe is not blocked, if it is you'll get a pressure build up in your tank.
Check your air filter element, if it is clogged you will have an over powering fuel smell and you may even have weeping of fuel vapours as it condenses.
Check all your vacuum hoses make sure they are in good condition.
If you have a fuel tap sometimes they don't seal correctly and weep fuel.

You can go online to NADA or Kelley blue book and check the value of any car, truck or motorcycle.

Hi ,

Please check that all coils do have a good earth as this could be part of the problem .
if you have power with the new battery i would suggest to trace the power source from the battery to the coil with a tester but the earth is usually the trick .
Please let me know if you have all lights working , horn and the starter is turning the motor etc...

Check out ebay or a list of dealers or scrap yards if you don't mind second hand.

Check choke is not sticking & when did you last clean your air cleaner unit .

pull back rubber boot on plug cap. unscrew cap and cut about1/8 inch wire and screw cap back on. Also take a flathead screwdriver and check clip in plug cap Don't tighten to much or you will crack the cap.

not that im a ware of  possibly could be your hose to the crank case breather is off or one of the hoses on the emissions fresh air intake under the tank  check these first