In the manual it is described to be measured in a different way, attaching the picture. It's a little bit confusing for me.I had a quick look here and couldn't find it in print. I do know that 14mm is a common height and I would beleive that to be right if no other confirmation is found.
Carlsalter.com had this supplimentary service manual. It doesn't list the float height but does have the correct OEM jet sizes. Being a 20 year old bike you may want to confirm the jet sizes for piece of mind.
There was a 1998 service manual but I don't know if the 2002 ran the same carbs. If you know other bikes that ran that carb and had the same cylinder angle you can use the same float height.
Free Yamaha Fazer FZS600(P) 2002 Supplementary Service Manual workshop service manual!Workshop Service Manual for a Yamaha Fazer FZS600(P) 2002 Supplementary Service Manual, free download from carlsalter.comwww.carlsalter.com
After opening carburators the only residuew was underneat the rubber diaphragm. What could be the cuase of that ?I have never done it as the manual shows. Like you, I typically like to set my height from the mating suface to the top of the float. I have seen people use clear tubing to check float heights visually and diagnose problems but it is a very awkward way to make precise measurements. In this case I would do 14mm and then check the height with tubing as the manual says.
I would be inclined to use some clear aquarium air line tubing and I would make two lines on it 4.5mm apart about8 inches from the end. Once you open the fuel screw, line the bottom mark up with the mating surface and the fuel should fill to the upper line. That will be way easier than trying to get calipers or a ruler in there.