Dear neets-  A)  double quench will result in finer grain size and therefore tougher at same tempered hardness.  double quench preferred where toughness is a critical factor e.g. impact loading or fatigue applications (gear teeth are typically a good example of both of these load conditions).
B)  These 3 heat treat methods would not be considered double quench since annealing by definition means slow cooling except in reference to solution annealing in precipitation hardening alloys.
C)  All three methods will achieve same approximate case depth.
1)  OK if distortion on quenching is not critical and toughness not critical.  Use where wear resistance is the essential property desired.
2)  Use where distortion control is critical.  This will tend to produce a spheroidal microstructure which is very stable and good for dimensional control to minimize or eliminate grinding after heat treat.  However, depending upon the steel alloy, it will also tend to precipitate carbides at grain boundaries and if a network of carbides results, it will drastically reduce contact or compressive strength within the case.  This is OK for sliding friction with low contact stress where dimensionsal tolerances are tight.
3)  This method is a compromise between method 1) and 2) in terms of dimesional or distortion control since it introduces a stress relief anneal between carburize and quench.  In addition, this process will result in finer grain size as in a double quench but to reiterate will reduce distortion compared with double quench because of the intermediate anneal.
    A good heat treating source can clarify this for you and I recommend you consult with one.  I would be very interested to know if any heat treater or forum member disagrees with any of my comments as I might not have it exactly correct.

Hope this helps,

Jesus is the WAY

All the above treatments will give you the same microstructure consisting of mainly martensite and austenite within the case transforming to a mixture of bainite and ferrite towards the core. Spherodising will occurr during annealing from 300 to 600 degrees, but this will be transferred back to austenite upon the second solution treatment above 800 degrees, and produce martensite on quenching. The % austenite will be dependant upon the % carbon that carburising was carried out at, i would expect a treatment as described to only give you a shallow to medium case depth, you do not explain what specification or material you are working with, generally a double quench and temper is used to rectify a heat treatment problem such as Retained austenite or carbides, where the lower temp and extra diffuse time allows for the carbon to become less saturated at the surface, you would generally boost @ 0.9/1.1% carbon atmosphere and diffuse at 0.75/0.85% carbon to obtain your desired case depth and structure properties, If you could highlight your application, component and specification I could indicate the ideal process required.

the material being used is 16MnCr5, which is a case hardening steel.
c - 0.14 to 0.19
mn-1.0 to 1.3
s- 0.04 max
cr- 0.8 to 1.1
 application can be like shakle bolt.
requirement of case depth can be 0.5 +/- 0.2 and HRC 58-63

A SUITABLE process if u could high light.

For the material you are using try
Carburising 900 deg C for 2 hours in a sealed quench furnace or similar gas carburizing furnace.

Lowerthe temperature to 780- 800 deg C to allow diffusion of the carbon from the surface and reduce carbon content to a level that prohibits retained austenite formation upon quenching. This procedure also refines the grain size of the material.

Warm oil quench, cool to room temperature then immediately temper at 180 deg C for 1 hour to reduce brittleness
Part should achieve 58 to 60 HRc.