That sounds like an electrical problem, not fuel. Being a Honda, I would say that your regulator/rectifier is on the way out and needs to be replaced ASAP as when it finally dies, it can take out your battery and other electrical components. Funky speedo readings is one of the first signs of imminent failure
The Honda R/R's are notoriously prone to failure as they don't have a large enough surface area to dissipate the heat generated. Don't get another Honda one or the same thing will happen. Try to get one from a Yamaha R6 , as they are much larger in size. The wiring may be slightly different but a bit of research will fix that.
The FI light is a bit of a worry as it may mean that damage has been done already.
One quick test is to check your battery volts when the bike is running. It should be at least 13.5 to 14.5V. If its 13 or less, then the r/r is suspect.