A constant beep from the fuel tank or fuel pump??

Could be your fuel pump or your fan is still running.

If it's the fuel pump. You should hear the same sound when you turn the contact on in the morning.
If you can only hear it when the bike is warm and you shut the engine down, it's likely it's the fan spinning. Some Kawa's do it, some don't. My old GPX600R did it. Sometimes it ran (after I shut the bike down) for upto 15 minutes (in hot weather),but my ZZR1400 doesn't do it at all.
My old GPX used to buzz/whistle form the gas cap too, but that shouldn't have anything to do with turning the power on/off.

Sounds like a blocked breather. Be careful with all that leaked petrol.

the best way to tell is take it to a motorcycle shop and have the error codes pulled from the onboard ecm.

there is a key hole underside of the left rear fairing, insert ignition key, turn and push seat towards the back of the bike. happy riding

To remove/unlock the seat on a Kawasaki er-6f find a circular hole under the plastic seat fairing half-way along the seat on the left-hand side. Using the ignition key twist the lock set in the hole

check the valve guide seals, theyre cheap to replace. does it smoke alot from the exhaust?

if you can see from behind the speedo casing, there should be a hole where the 2 wire goes in. Now you must remove 2 or 3 screws that hold the 2 half piece and inside of it you will see the location next to speedo cable.

See my answer above

Yes, you can get a kit to rebuild the master cylinder. Talk to the parts department at your dealer to get the part number.