As dmoz is listing only sites which they think useful for others. They may not approve any of site. If your site is very establish and useful then only they will approve in 2 week to 2 months.
Suppose if they consider my site is not useful, they will intimate it to me ? Otherwise is there any possible ways to know the reason for not approve my site.
I think here is the answer to your question, only when your site is useful and well-established, then it can be approved. there is no need to give detailed reason, that really a lot of work...
DMOZ's Editor has visited my site just a week after i registered with them. Please read this topic: http://forums.digitalpoint.com/showthread.php?t=1437367
That is all false information. A site may be reviewed and listed in two days to three years, if at all. The Directory allows you to suggest any site, but editors are not required to consider them, we have many resources to find new sites, and we don't want all sites. Editors are only interested in the "unique content" on a site, nothing else. If you don't have it you won't be listed, and no, we will not contact you with an explanation. That's just not feasible for us to do. Once you've submitted your suggestion, just forget about it, there's nothing more you can do.