Where do i oil the throttle cable

check clutch cable adjustment as it sounds like the clutch is slipping

oil and filter regularly
air cleaner
plugs
coolant level
check brake fliud\ brakes for sponginess(bleed if necessary)
throttle cable is smooth and closes by itself
brake pads for wear
chain adjustment
drain carb bowls
check all lights
check tyres and pressures
Check wheel bearings\swing arm bearings
Battery water
General nuts bolts and screws tighten


and at lesser intervals
carb adjust
valve adjust
coolant change
brake and clutch fluid change
fork oil change
head bearing adjust and grease
rear suspension grease

It has automatic choke driven by engine vcuum. Good?

Sometimes ,if a bike has been store up over winter ,,the carbs can get or become very sticky ,this is generally cause by damp or the fuel gets sediment forming in the jets .if your bike is getting stuck on the throttle .,the best thing to do is to strip down and check that the carbs linking arm is not stiff or rusty ,and while you are doing this remove the throttle cables and give then a good soaking in W/D 40 or equivelent and re oil the inner cables ,Cables can be olied using a baloon filled with thin oil and attached to one end using sticky tape and hung up and allow the oil to soak through the inner cable .You can also give the inner cable a push & pull movement to help the oil get right through the cable ,till it comes out the other end .

Here is a diagram showing the tubes you connect your vacuum gauges to.
http://216.37.204.203/Yamaha_OEM/YamahaMC.asp?Type=13&A=326&B=11
The YZF600R is carbureted, so I do not know what you mean by throttle body adjustments.
Synchronizing carburetors means adjusting the throttle plates (butterflies) so that all cylinders are drawing the same amount of vacuum.
Here is a diagram of the carbs. Screw #31 is the screw used to change the sync.
http://216.37.204.203/Yamaha_OEM/YamahaMC.asp?Type=13&A=326&B=13
Remember one other key point, all carbs are sync'ed to the #3 carb. You cannot change the vacuum (directly) on #3. It is usually best to start by syncing #2 to #3, then #4, then #1. Changing #2 can affect the sync on #1 so you definitely want to do 1 after 2 no matter what. If you have one cylinder WAY out of sync, that would be an exception to the previous rule where you would want to attempt to get that cylinder in the ball park of the others before fine tuning each cylinder.
Syncing the carbs is an alternating process between adjusting the vacuum then adjusting the idle. If they were out of sync, bringing them back in, or even getting close, can cause the idle to raise because the engine isn't fighting itself anymore. Always keep the engine idling @ 1100 rpm's while syncing.

it sounds like your fork seal has failed,it wont affect your brakes but will make your front suspension feel a wee bit "soggy"and will affect your handling,i would suggest getting the seal replaced as evetually the oil from the faulty seal will contaminate your brake pads that will affect your braking performance,replacing the seal,sooner rather than later ,would be a wise move..hope this helps...cheers

Inject some carb cleaner spray through the opened air filter while cranking.
Spark plugs work? timing on the camshafts ok?
Crank it without turning the throttle on.
Pull the choke cable if you need to.
It should fire up without throttle.
Use the carb cleaner spray to help it (don't spray too much.It will backfire from the carbs).

I don't have a service manual on your bike BUT if you Google " yamaha yzf 600r " there is a spot 3rd from the top that has a free download if you can open an RAR file.