your pictures are too small to tell
Wire colors and factory service manual will help you but in the meantime i suggest going to a junkyard and get the piece of harness that burned, splice in at the point where yours is intact and should be fine - solder and shrink tubing over it will make a sounds repair with no issues in the future. As far as vacuum tubing just replace them (or whatever tubing got melted, looks like one of them is the PCV tube - the one on top of the valve cover).
If your question is if you can drive it like that, i wouldn't, you should repair whatever got damaged in the incident.