Your "tuner" is mis-informed IMO, and has caused you a major inlet problem to boot, it's possible all that leaking air may have burned something inside Oil could be sump gasket, plug, pump seal, crank seal? Not likely to come from the H/G as the feed hole is in front of the block near the oil sensor
The front of the engine and covers look bone dry. I ordered some GTE intake manifold studs at work today. I am going to put those on anyway, but could all the smoke and running issue be from the loose intake? Maybe oil burning and not coolant? It looked pretty white to me, but the res and radiator are not low and it didn't overheat.