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I just got back form the gym (working out and wathcing TV) and the folks on Fox were throwing around the term “angle of attack” without really knowing what it is. Even their “analyst”, Dr. Gross, seemed to be confused.

I think the fact that the plane was fully loaded may be significant for weight and balance aspects. The plane should have performed even if all seats were filled, it would probably not have had a full load of fuel particularly for such a short hop. But any stall immediately after takeoff is usually a weight and balance problem. If the airplane's center of gravity is too far aft of the allowed range, the forces on the plane's horizontal stabilizer will be inadequate to prevent the nose from continuing to climb until such a point at which the angle of attack is so high that lift is substantially impaired.

CVR should show sound of stall warning. I don't know if this plane has a stick shaker, I would doubt it.

Sure, other things could cause a stall, spin, inversion sequence: wake turbulence that was severe, even the pilot's seat sliding back suddenly as he is holding the yoke.

Icing is unlikely since no matter how much ice might have formed or wherever it formed, it would hardly cause such an immediate and catastrophic effect. Carburetor icing is largely a fallacy anyway, 99% of the time it doesn't exist!

Its obvious that the engines were developing sufficient power for the takeoff roll and rotation, but if anything happened to them (or worse, to ONE of them) the pilot should have been able to deal with it.

A low time, amateur pilot suddenly faced with loss of an engine on takeoff might react slowly or incorrectly, but under no circumstances would a professionally trained pilot be unable to deal with an engine out situation on a twin.