Overdue Oil Change and Sludge, safe to drive after oil change?

The fact that the lack of oil pressure light turns off means nothing. It takes very little oil pressure to turn off that light and while the light may go out that does not mean there is enough pressure to safely protect the engine.

Black oil, less than half a gallon of oil in it means trouble ahead and any oil consumption issues are going to get worse.

Not a car I would recommend taking on a road trip and unless he gets in the habit of checking things under the hood every week or so his automotive longevity future is going to be dim.