I am not sure why the red light is on (I assume that you are referring to when the bike is running), but you can figure out why the FI code is on. All of the sensors on the bike report back to the computer. If one of the sensors reports an unusual reading, or doesn't send back a signal for 2 seconds, the FI light goes on.
In the tail section of the bike, you should find a white plastic connection on the end of some wires that is not connected to anything. Only two of the four 'holes' in the connector have plugs. Use a jumper wire between the two with the key in the on position when the FI light is on and it will give you a code on the dash. (It will read a C with a two digit number after it. C28 for example.) That should give you an idea what the problem is. I can look up the code in my service manual for you. Or, you can find the codes online. (The codes are the same for all Suzuki FI bikes)
Get that info first and you can go from there.