2000 GSX-R 600: my 2000 gsxr 600 keeps shuting off i rchanged the ...

It sounds like its possibly a bad regulator/rectifier. I have posted a link to a video on how to test your regulator. How to test 2 plug Regulator Rectifier for K6 K7 GSXR 750 600 1000

Could be ignition fuse. If not that then check the large block connectors which are usually located on the left hand side at the front of the bike behind the cowling beneath the handle bar. These connectors are notorious on GSXR's

you need to replace the air temperature sensor. looks like this one https://www.ebay.co.uk/itm/Suzuki-GSXR-TL-SV-AN-600-750-1000-Air-Temperature-Sensor-1996-2009-13650-61B00-/182447458716?hash=item2a7ab7499c:g:-rYAAOSwopRYmblq

THAT WWOULD DEPEND ON HOW MUCH THE DEALER YOU TAKE THE BIKE TO CHARGES PER HOURS LABOUR, FAIRLY EASY JOB

No not without modifying the base - very difficult

Hope this helps (if so please mark as very helpful)

Ride Safe
Bike-Doc

have have the same problum when you find out can you call or text 772-204-3186

try replacing the fuel filter.