2000 Yamaha R6 Starts and Idles but problems with the choke

sounds like it has low compression or that there is something blocking fuel from reaching the carbs try a new in line fuel filter if that doesnt fix it clean the carbs and tank and fuel lines out with brake cleaner also do a compession test first and check with manual for specs.

2nd gear is a problem that has plagued the 2000 r6 have a pro look at it or go to yamaha r6 forum and they hav the how to's on self repair i hope your sitting down its not a easy or cheap fix.good luck!

Sounds like the idle circuit in your carb is restricted or carb is set too lean. Good fuel and new filter is a must

Yes. Sounds like main jets are blocked. Gas will start to varnish after a couple of months. This builds up over time and sticks the main jets. Go to this website and select discuss this bike.http://www.bikez.com/motorcycles/yamaha_yzf-r6_2000.php