Pcv bypass and carburetor hook up

Here is a general fuel line diagram for a 1990 Suzuki RF 600 Katana:

1. Fuel tank: The fuel tank holds the gasoline and is typically located on top of the motorcycle frame.
2. Fuel petcock: The fuel petcock is a valve located on the bottom of the fuel tank that controls the flow of gasoline to the engine.
3. Fuel filter: The fuel filter is located between the fuel tank and the carburetors and helps to remove impurities from the gasoline.
4. Fuel lines: The fuel lines connect the fuel tank, petcock, fuel filter, and carburetors together in a specific sequence.
5. Carburetors: The carburetors mix the gasoline with air and deliver the mixture to the engine cylinders for combustion.

The exact fuel line routing and connections may vary depending on the specific model and year of the Suzuki RF 600 Katana, so it is important to refer to the owner's manual or a detailed service manual for accurate information. Additionally, any modifications or repairs to the fuel system should be done by a qualified technician to avoid damage to the motorcycle or injury to the rider.

fiddly job
but easy to do
remembering what bolt and plug goes where
you will have to remove your petrol tank and air filter box
fuel tank has 3 bolts 1 at the bottom 2 at the top by the head stock
slowly remove the fuel tank remembering to turn off the stop tap
and remove the fuel pipe and the fuel gauge sensor wire

air filter box
under the air filter box
there are four banjo clamps
that hole the air intake tubes to the carburetors
undo these four screws and remove the air filter box

you will then see where your idle cable is located
just replace the idle adjust cable and reassemble the
air filter box and fuel tank in the reverse way you took it apart

GSX 600F Katana 1989-1991
GSX 600F Katana 1989-1991
OEM Gear Ratio - 14T Front Sprocket / 46T Rear Sprocket OEM Chain - 530 Pitch / 112 Links

replace the fuel
clean the carbs
change the oil
new plugs
clean air filter
check the valve clearances( if any are really wide a valve may be stuck open)
I assume you have already fitted a new battery

Changing to a K&N air filter changes the air/fuel mixture for your bike, and you're probably hitting an overly lean spot before things start to even out. For bikes still running carburetors, which I think you have, you can compensate for this by changing to a slightly larger idle jet. Your main jet is probably fine (it's kicking in after the lag); it's the crossover from idle to main jet that's causing the flat spot.
Talk to your dealership parts counter to get recommendations about jet settings. They may suggest, for example, to keep your existing idle jet and go with a different main jet. Expect to try a couple different setups to find one that works best for your bike and your riding style. I would highly recommend keeping your original jets, though, in case you ever go back to the stock air box.

replace the fuel filter

You need to re-jet your carburetors to compensate for the increased air flow. The bike is starving for fuel because the carburetors are jetted for the air box. Typically you would need to change the pilot jet and adjust the a/f mixture on the carbs. You didn't specify if your carbs were stock or modified so I am including a link for you that can guide you through the process. In the meantime, if your bike is a daily rider, put the stock air boxback on until you can re-jet the carburetor. Here is the link: http://www.dynoman.net/carb/pdf/mikRS-access.pdf

I guess you need a new ignition switch to cure your turning off problem, the pipe from air filter is probably the crankcase breather that vents pressure from engine in to air box, this will contain some oil mist