This is not just one question but a series of questions. I will attempt to answer the questions.
Do they call and check with the hotel ?
Based on empirical evidence from around the Web, they DO call and check.
The embassy asks for the complete travel itinerary with booking confirmations. Do they use the booking code to check the airline website if the booking actually exists ?
My travel agent advised me that for Schengen visas, the booking should remain valid at least until a visa has been issued.
Based on a Twitter conversation with an Italian Consul-General, everybody knows that hotel and airline bookings are regularly changed after a visa has been obtained. Any change in the rules would require the approval of 26 countries. Any attempt to change this ridiculous and pointless rule would have to pass through several bureaucracies.
Generally Is there a single person who looks at a visa application ? or does their visa approval process involve going through multiple people always ?
During my last application, I apparently had missing documents. The interviewing officer told me that all supporting documents are uploaded to a system and my application would not be processed until that missing bit was submitted. Who looks at the documents after submission is difficult to pinpoint and probably defers for each consulate but it's highly likely that more than one person is involved. Unlike the UK and USA, the final authority to issue visas is with the Consul General.
How much time do they spend per application on an average ?
This obviously differs for each consulate. For example, in the UK in 2009, it took 11 minutes for the final decision-maker to judge applications from Pakistan. The total involvement time if you include background checks made by other staff is much more.
Do they do a credit check with credit check agencies (like CIBIL, experian) to see the individual's liability and credit score ?
That probably depends on local privacy laws. It is highly unlikely that a German consulate would run a USA credit check for an applicant applying from India. I am not aware of the privacy laws in India.
What other backend processes are involved in the life cycle of a visa application ?
This is an open question. Among other things, they may call your bank, employer, run your name through Interpol, and the SIS and VIS systems. These checks are made to verify the authenticity of the documents submitted and statements made. However, the Schengen visa process does not make as many background checks as the British and Americans.
What is the qualification of a person who reviews a visa application ? Bank statements and income tax returns are also submitted by me - so are they qualified enough to understand balance sheets, capital accounts summary etc. ? Or is there a process where an application is run through a financial eligibility check (with an accountant maybe ?)
It's within their job description to evaluate bank statements and income tax returns. Don't underestimate them. They are smarter than we think.
Do they go through past schengen itineraries to check for overstays (by comparing with stamps in passport) or they have this information already calculated by entry / exit scans ?
This is an interesting question. According to Wikipedia (it cites four sources): SIS does not record travellers' entries and exits from the Schengen Area. This means that they would have to rely on manual stamps to figure out an overstay. The Schengen countries have physical exit immigration controls and you are more likely to have trouble trying to exit than trying to apply for another visa. If the consulate has doubts about your intentions, they may have asked you to appear before them AFTER you have returned to your country to confirm that you conformed with the visa.
Schengen countries are very concerned with privacy. Unlike the UK and USA, the VIS only retains information--including biometrics--for a maximum of five years. I am not sure if the VIS includes your submitted itinerary, but I think it is unlikely.
The following document provides a general guideline for how the data collected during the application process is stored and used.