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I will try to help you the best that I can, from my knowledge of the visa process and having successfully applied twice. However there are many circumstances that affect the visa process, and some countries are more accepting than others.
1.I have the NOC from the present employer (for 10 days leave), though I have just completed 3 months. Would this short tenure be a concern when processing our applications?
No, it will not. People move jobs all the time. Remember that you have to convince the embassy that you are a genuine temporary visitor, and not trying to immigrate.
2.My family UAE residence visas were stamped only 15 days ago. (Please note kids were born in UAE and past 9/10 years they all were living in UAE). Since the new residence visa was just stamped, will it have a negative impact by the time of processing our applications?
No, this has no impact. Again, residencies are renewed all the time.
3.Five years ago when I was with the previous employer, I was assigned in Afghanistan where I stayed for 4 months, solely for logistics functions and coordination with the U.S. military. So Afghan visa has been stamped on my (previous) passport. How can this affect my application?
It has no bearing (I was in Iraq for a similar logistics client).
4.Should I submit the previous passport too along with the application?
Only if you are specifically asked for it, or only if it contains a valid visa. Otherwise your old passport is not relevant.
5.Does it require to mention the above point No 3 on the cover letter or not required?
There is no cover letter required for a Schengen application. The requirements are:
6.If required to be, I can get a letter from the previous employer. Is it advisable to get the said letter and attach it along with the application?
No, what would the relevance be? There is nothing that your previous provider can furnish.
7.How much of bank balance would be considered as a healthy limit for a family of 5? (Planing to travel to Rome and Venice for a total of 10 days)
Each country in the Schengen zone has its own minimum requirements. This PDF (in Italian) has a table that lists the fund requirements for visitors to Italy.
It states the following minimum amounts as translated from the PDF using my very rusty Italian:
Please do not park funds in your account. This will almost certainly get your application rejected as its considered a form of fraud.
8.In case if a visa is rejected will the Italian consulate straightaway endorse the rejection stamp on the passports or, they will call us for an interview to discuss further and then decide to approve or reject?
No, there is no such process. Either you are approved, or you are rejected. If they have any questions about your documents; they may ask for additional details (this is usually a good sign).