how do i check these problems? how can i fix them?
First, get the PDF version for the Busa service manual. Search "Hayabusa manual PDF" and you should find it. It appears that it was removed from our oRg site here, but I'm sure you will find it somewhere using Google.
I recommend pulling all the spark plugs to have a quick look (as I posted earlier). Keep track of the position of each plug as you pull them (label them by each cylinder number).
You can find guides to reading plug condition in any Chilton's, Clymer's, or similar manual you have. Or you can search "read spark plugs" and find lots of examples on the web. Note that these pictures are usually for extreme examples. Usually they don't look that bad! On an engine that is running mostly correctly, the changes will be subtle.
Look at the ceramic insulator surrounding the top electrode (the round one in the center).
1) The insulator is noticeably lighter in color on one plug: Indicates a lean running cylinder (too little fuel) and points to a fuel injector that needs to be cleaned.
2) The insulator looks dark and sooty, often accompanied by dark/black soot on the bottom (bent) electrode: Indicates two possible conditions.
a) the cylinder is not igniting consistently due to a weak ignition (most likely, and suggested earlier by others); or
b) the cylinder is running too rich a fuel/air mixture (less likely on a fuel injected engine, but certainly possible if a fuel injector is leaking).
You can do one more, even easier test. Take off your side fairings. Start and run the cold engine for about 30 seconds, then shut down. Take rag to protect your hand and touch each exhaust header pipe near the engine. See if one cylinder feels cooler than the others. That might steer you towards a poorly performing cylinder before you pull anything apart.