No, do not replace everything.
Do you have a proximity based AC detector?
Do you have a signal-toner? (wire finder)?
What has changed (if anything) recently with respect to light fixtures, wall outlets, switches, extension cords, etc? Especially and obviously on this circuit specifically? Did you add/remove anything new? (a heater, an AC...)
The flickering for the bathroom light fixture that no longer works was probably your indication of a problem where somewhere a splice is detached (wirenut, backstab, wall sagged and tore some romex)
Has there been any new work activity in an attic or a basement?
Anyways....
As/If necessary, isolate all power and either use a toner or a detector with the goal of identifying all points of wire junction on the circuit in question. Positively identify anywhere there could be a BOX (switch, outlet, light etc.).
Using the above, make a logical path from the circuit panel to each room. Where would you run the wire FIRST if you were an electrician and didn't want to waste money on wire? Focus more on any common points near the affected area. NOTE: common sense doesn't always apply with how they run the wire, but it's a good guide.
Mark off any items that had "a lot plugged in" or that people bump/wiggle a lot.
Secure power to the circuit in question if not already.
With your list of suspects, (key suspects are ones that were not working) take a wall plate, or light fixture off and pull the wiring out. Ensure all wirenuts are secure, nothing is loose, burned, or dangerous looking. If so, repair it.
Pay close attention to any non-ground wires under a wire nut (more than 2) or in a backstab (more than one, or better yet, NONE!) or double upped on a screw.
If backstabs are used, take the time to correct this.
If wires are more than one to a screw, correct this.
If there are more than 2 wires on a wire nut, inspect it. One of these wires may be the suspect causing the outage.
Do not resume use of the circuit until you identify the bad connection. It is a fire hazard.
Depending on what you find from the guidance above, you might want to do the whole home. The issue you are having "should never happen"
Lastly, and this could have been first - do you have aluminum wiring? If so, there is a completely augmented list to follow.
Best Answer
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.