Can you tell me if Neutral wire is burned?
To me it looks like the wire may have been loose in the past and retorqued notice the gouge in the wire a torque driver was not used to do that much damage to the wire. Since you are having flickering or lights / circuits out and you have checked the panel it is time to find the problem. If you have other outlets or lights on that circuit that are working the problem will be at the last working outlet or device or the first non working one.

The most common cause is a back stab connection being used, these are when 14 awg wire is used and just pushed in to make the connection ( not under a screw or clamp), the next place is broken wires at a connection or 1 wire pulling out of a wire nut. I listed them in the order I find them in over the years. The big problems with back stabs is they may look fine on the outside but with a failed connection there is usually some deformation of the plastic and or insulation but you may have to look close. When you find the problem if the insulation is intact cut the arc marked wire back to good copper, this is enough as only the loose connection area was heated not the entire wire. 

There is a small chance the problem could be a bad breaker, or panel and an even smaller chance it is a very old MWBC that did not have handle ties and the 2 breakers got separated and put on the same leg. To see if it is a MWBC trace that white wire back to the cable coming into the box. If there is only a black you are done. If there is a black and red (the most common hot colors) trace the black and red back to their breakers. They should be next to each other and by today’s code have handle ties, or a single handle, many years ago they just had to be in adjacent slots. If this is true the panel wiring is correct. If the breakers are separated someone messed up and they need to be together a handle tie or double pole breaker is the safe way to go. 

Go back and find the source of the problem it usually is the last working outlet or device or the first non working outlet or device.  And it could be the white or hot wire at those locations.