I think I am able to find the root of the problem.
I have installed another plugins called wp-report error which also have the same problem. When I click on the link to "Report Error" the pop-up window is not opening.
So, in my inspection the problem is with the pop-up scripts. Somehow it has been blocked and that's why I can't see the FEE edit window or Report-error window. I have cross checked my browser settings for the pop-up blocking options. But, the problem is not with my browsers. May be it comes from my server.
As I am not an expert of coding and scripts or in website development I can't solve my problem.
Could any one here give me some suggestions to resolve my problem? I'll be very thankful to him.
N.B. The slide show pop-up window for NextGen Gallery is working fine with my site.