DNS not resolving local addresses

     I'm pretty sure you will have to set up local addresses manually. I don't have the need yet myself, and will be interested in exactly what people come up with for an answer to this, so I'm subscribing to the question.
     If no one else comes up with anything based on experience, I'll be happy to look through what I have and try to work it out with you.
     If you accept this as true and manage with your own research to come up with what you need, can you please post the basic steps back here for me (or for us)?

On set up the server, it resolve all addresses both local and external well on the server itself but from the computer relying on the server for name resolution the local addresses are not resolve exempt for dig and lookup but not ping and in web browser.

     Well, just browsing and find some info at http://www.aboutdebian.com/dns.htm that indicates your local network has to be set up. Most DNS name servers are going to have public information about what is available over the internet, but not on your home network (unless you are going to publish them and therefore not going to have a private network). Mention is made as well of using the HOSTS on a local intranet like that, and info is available with "man hosts" that shows how to manually set up a host name resolver.
     Again, I don't have the need right now, so hope I will not be the final source... I like my answers to come from someone else's EXPERIENCE DOING rather than what people have read, but am responding in case no one else has info to offer either.... and in hopes it might serve you well (might answer your question).

Thanks Larry Jordan, the documentation you refer to is very rich, so I am taking my time to study it. Meanwhile I now discover that if just use mail instead of mail.sadeeb.local it resolves perfectly but using the full name will not. Is this how it design to work on local domain?

     I believe so; studied it when I had Fedora Core 2 but never made much use of it. Try to stay in touch with it now because I have 2 children and a wife using this computer also, so may HAVE to get another someday and network it. Seems like quite the process to me, but only chance I ever had was trying to connect one computer in Windows to use another using Windows XP. XP made it easy enough to connect a second computer such that it would "take over" the other, and run everything that was on the XP computer, but wasn't ANY kind of a network. So I'm fascinated by what you are doing and glad to provide any help I can.