Electrical Outlet arc burned the wire. Do I need to replace the entire line?
The rest of the NM cable should be fine. When I install outlets like this, I pigtail the wires and connect the single wires to the outlet and still use a shepherd's hook behind the clamp.
The closeness isn't a problem if done right. You can have a split outlet with different legs so you've got 240 volts just that close.