So, I have a hypothetical aircraft that needs to get from FL350 to 10,000' as quickly as possible.
Airspeed control is the difference. In a rapid descent, airspeed is controlled and the pilots will keep it below $v_D$, the maximum dive speed for which the aircraft is certified. For a modern airliner, this is somewhere around Mach 0.9.
In a dive with "nose down as far as they care to" (I read this as 90°), airspeed is not controlled, but an outcome of the situation. The airliner will go supersonic. It is possible to recover it from a short dive, but will incur damage to the aircraft (e.g. the pilots will need to lower the landing gear to increase drag, but lose the gear doors in the process).
If the pilots would only care to put the nose down to the point where they not exceed $v_D$, we are back at a rapid descent. They could lower the gear in order to increase the sink speed, and circle to increase drag further. Circling needs more lift (proportional to the inverse of the cosine of the bank angle), so more lift-induced drag is produced. To maximize drag, the pilots should fly at the maximum permissible load factor (which is rather low at maximum dive speed due to gust loads).
If we assume the L/D of the airliner to be 5 with gear and spoilers deployed, the pitch attitude would be between -11° and -12° and the sink speed would be between 50 and 60 m/s (10,000 to 12,000 ft/min). The bank angle would be between 45° and 60° and the plane would be violently shaken by buffeting.
Going any steeper than that would only be attempted by pilots with suicidal leanings. Flying like described above is scary enough already.
'Dives' in an airliner should really be avoided at all costs.
A nose-down dive could have the following dangers, just to name a few:
The standard emergency descent procedure will get you to a safe altitude quickly enough, with oxygen supplemented.
I'm sorry I can't answer your other questions but I hope I have explained why a dive would not be a viable option.
A nose up descent with a low airspeed is best.
I did one on my multi engine instrument flight test. The examiner thought it was great.
You pull back on the power to idle.
Raise the nose like you are wanting to enter a stall.
Let the airspeed wash off.
As it approaches maybe 10 or 15 knots above the stall, you keep the airspeed there by lowering the nose.
Normally when deliberatly entering a stall, you would continue to lift the nose until a wing drops.
But you lower it. To maintain a speed above the stall.
The lift has already reduced enough so that the aicraft will descend.
But it does it with a nose up.
Airliners do it on every landing, but its being done with power applied and so its a gentle desvent.
If you wanted to drop from the sky when you are way too high on an instrument flight test, its best.
You will drop like a stone and have a extremely steep angle. With very little ground speed.
If you want to get some airspeed back fast, just lower the nose and apply power. It you want to arrest your descent. Just slam the power levers forward and you are already in a climb attitude.
Its not for the kind of pilot who is not confident. But if the plane is part of your body, you will get it naturally.
