Can i search for files even when the application is closed?

The first secion in http://dcplusplus.sourceforge.net/webhelp/window_search.html tells you how searches work in DC and will probably answer your question.

"The Search window allows searching for files inside the shares of on-line users".I was asking that can the search function be made to work for all the users of a hub irrespective of the fact that they are offline or online. Also, Can the search be made on the all the hubs listed and stored in a local area network?

I thought the link will answer your question. It is definitely no.
DC clients (as the network/protocol name says "Direct Connect") can only communicate directly or by using a relay function provided by a hub if necessary, and only between online peers.

I don't understand your second question.

I am asking that suppose the user is not connected to a hub but has listed that amongst his favourite list or so , so can the search work on that hub? I am asking this as I am thinking about a notifier plugin which notifiy the user whenever a new file is uploaded which the user queried for and wants urgently like the new episode of a sitcom. so rather than searching it manually on a regular basis , he can just type in a query at a earlier time and whenever he opens up dc++ the next time he gets a update about whether that file is uploaded or not.

You can search on connected hubs only and as I said the hub serves only as a relay between clients logged in at a given time. A DC hub itself does not store any information about shared files of any previously or currently connected clients.

BUT there are apps like "easy dc search"(http://home.deds.nl/~dcsearch/) which achieves this, is that true or not?

Well, I've never heard of this "software" but reading
"DC Search is searching more than: 10000 DC++ hub servers * about 120000 - 560000 GigaBytes of information in each hub"
in the website this should be nothing but junkware if not some seriously malicious stuff.

The public DC network currently consists a lot less DC hubs (there's no such as DC++ hub anyway) and it never had more than 300-400 public hubs even in its heydays...

Theoretically it's possible to gather information of every share of every connected hub but that needs a constantly updated, fresh central database on a server that runs a software which acts as a DC client, keeps itself connected to every public DC hub and downloading all hub users' filelists in some intervals.
If the above program is valid then it does probably something similar but I doubt it'd work efficiently since hub owners would rather ban such fake clients as they'd need to generate some very big filelist upload traffic while there's zero benefit to the usercount.

But wouldn't this be feasible for a dc hubs in a local area network only (something like 7-8 hubs atmost) ? Just asking for a suggestion if it can be made feasible.

Well, such software or DC plugin can probably be made.
I'm not sure the current DC plugin interface propagates everything you need to make a plugin that automates file list downloads from every user of every connected hub.
In a LAN environment high file list traffic would certainly not be an issue.

Also, if a user is offline then we can't download his entire file list , can we ? Also, what do you think that would there be any utility of the notifications (the DC++ notifier) . One utility i can think of is that the user don't have to type and search for his files on a regular basis instead he will get auto generated notifications. So, what's your view about this plugin ?

Thanks for all the support!!But can you please answer my last question?

Thanks eMTee, that solved my question.

sorry, but that was one of my friends!
about that automated file list downloading , implementing that for a novice like me(but well aware of c++) would take how much time approximately if i work on that devotedly ?

See my other answer about the focus of this support place.

If you want to discuss your development ideas further, I suggest using the central DC development discussion places such as http://dcbase.org or the DC development hub at adcs://hub.dcbase.org:16591 (temporarily offline atm)

I am not able to access DC development hub at adcs://hub.dcbase.org:16591