The first connector you pictured I can not find on the wiring diagram, Without more info I have no idea what it is.
The second one that might be a blue yellow and a black yellow in which case it could be two of the four wires that go to the clutch switch and is the starter circuit cutoff relay. Some one may have had issues with that and bypassed it. Again that switch is known to get dirty contacts. If it is bypassed then it means that you can now start the bike in gear or take off with the side stand down. Both potentially very dangerous.
The computer acting weird could be an issue with the gear selector switch, there is a 6 pin connector between the switch and the computer, make sure all of the contacts are clean and you can test the switch with an ohm meter. one lead to ground and the other to each of the 6 wires. when the switch is in the position for the wire being tested ot should be near zero ohms, all the other wires should be infinite.