Put the jump leads back on and fire it up again. remove jump leads and while the bike is running check the voltage across the battery. At tick over it should read approx 13.5v and if you rev it to approx 3500rpm it should rise to about 14v. If you get these readings then the reg/rect is working correctly and you have a duff battery
Maybe....but they are not know to go on the fazer.Lift the tank and check the white plug with 3 pairs of white wires going into it located approx above gear pedal under tank. Any melting or burning there and that will be your problem. This is a know problem on the bike