The drip from the oil cooler line doesn't sound like a major problem. Could just need to be re-torqued, or the seal washers replaced.
If your bike doesn't visibly smoke or use a quart or more every 600 miles, a warranty repair will be hard to get unless you happen across a very sympathetic dealer. (Some folks have.)
Also, if your VIN is JS1GV77A*22102179 or higher, you already have the newer pistons.
I would be surprised if it is running rich. These bikes normally come from the factory jetted very lean - to make the EPA happy.
Yours is a 2002, right? AFAIK, the only difference between a 2001 and a 2002 is very minor. The difference is in the digital displays in the speedo & tach. The '01 has a fuel gauge in the tach and the digital clock, odo and two trip meters are all in the speedo. The '02 put the clock in with the fuel gauge. So, unless you're dealing with the wiring to those functions, everything is the same. My guess is the service manual is the same for all '01-'05 models and just supplements to adress the minor wiring changes in the later years. (There were a couple more minor wiring changes in '04.)