How's the radiator itself look ? Not full of dead bugs or the fins all bent ?
Losing coolant is usually a sign of the head gasket leaking but it doesn't sound like the problem from what you descibe .
The timing being off could be a cause , have a look at the spark plugs and see what they are like .
If there was no other damage and you put a new timing wheel on , it should start . The timing wheel should only go on one way .
Make sure there's no metal fragments around the timing sensor .
The FZ6 has a chunkier timing chain and gears so to fit the cams you need to use the FZ6R cam gears because the gear on the crank is different to . The FZ6R cam gears need to be machined to fit on the FZ6 cams and the holes need to be slotted so the timing can be set to 102/105 . The gears are...
You can get away with not slotting the gears but there will be a bit of a flat spot down low . The timing Marthy quotes works the best . Pulls from 4000 rpm to redline .
Don't know why the idle changed but it won't be because of the exhaust change .
There's an idle adjuster screw on the left side of the bike . Look between the frame and panels near the throttle body for a phillips heads screw.
Not sure what your trying to do .
It will start in gear if the the clutch lever is pulled in , but not if the stand is down , there's a switch on that to .
Australia might be the only country that had the restrictor to comply with the learner approved power to weight restrictions. Go into diagnostic mode on the dash and see what your throttle reading goes up to. Restricted was 70%