Godaddy to BigRock (Domain Transfer) How long does it take ?

Also, by default, what DNS record the new registrant set ?? Will it copy the details from Godaddy or it would set its own records and I manually have to change those once BigRock gains control and grants me access to modify details..

As far as I know, when you move your domain from godaddy to bigrock, the nameservers will be set to the DNS nameservers of bigrock, i.e. ns1.bigrock.com etc. You will have to using the DNS management tools on bigrock to add the required records like cname, mx etc.

Site may rather will face down time then

Even IB had to face downtime while shifting to a new server 

I never had any down time while changing server as only thing I had to do was disable the comment system till DNS transfer was complete, site was accessible for all..

There is always some down time associated with domain transfers. You need to consider the fact that DNS transfer and propagation throughout all the ISP's throughout the world takes time. Usually, 24-48 hours for the DNS updation to be completed throughout.

I am not sure, but few years back, when I transfered from Yahoo to Godaddy, at time of transfer I think, Godaddy asked for public WHOIS, whether to keep exisiting as per the releasing registerer or set their own, but here, then taking the domain from Godaddy to BigRock, BigRock asked nothing so confused about it..

Today I have received a reply from BigRock on a support ticket which i created regarding this issue with the same question. Following is their reply..

This is inform,you that once the the domain transfer is initiated, and transferred to us all the entries including the DNS entries will remain unchanged.Only the company owning the domain will be changed.All the data under the domain will remain the same.

It seems, they don't change the public WHOIS records..

The transfer is done.. It seems they didn't touch the public whois record, including the DNS.. The old records are carried forward.. No down time faced..