What is the benefit of the double feedback of the LMV324 op. Amp.? Why was that implemented in that way?
From this scheme I have to understand why was implemented in that way 
Answer
It is one of the most challenging tasks to design a high-gain amplifier for frequencies down to zero Hz (that means: DC). The reason is that in this case, we cannot use coupling capacitors between the several stages (which would allow us to design and stabilize each stage separately). Each DC offset of one stage will act as an unwanted input for the following stage.
Therefore, it is absolutely neccessary to DC stabilize each stage using internal DC feedback. That means: It is a stabilization against an unwanted shift of the DC operating point - not against oscillation! In contrary - each feedback reduces the phase margin; that is the price we have to pay for a stable DC operating point.
Now, we have a high-gain DC amplifier and we want to realize the final gain value. For this purpose, we must use an external overall negative feedback loop (from the output to the inverting input). Again, this feedback loop will reduce the overall phase margin - and to avoid oscillation the amplifiers internal frequency response must satisfy some specific requirements...but this is not part of the question.
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