Recently I tried to catch requests from Internet Download Manager using Fiddler, but it doesn't seem to work (but works fine with other requests). I also try to catch requests from a file hosting link getter but it doesn't work also.
Later, I try HTTP Debugger Pro and it catches all the request from IDM and the link getter like a charm.
The question is why HTTP Debugger Pro can catch all the request but IDM cannot? Any work around to solve this problem? And how to procedure requests that Fiddler cannot catch using C#?
To elaborate on SLaks' comment: the extensions in question are buggy, and are not properly adopting the system's proxy settings. As a consequence, traffic isn't sent through Fiddler, and thus isn't seen.
Some apps and extensions offer a way to manually set their proxy setting; if you adjust the setting to 127.0.0.1:8888, the traffic will appear in Fiddler.
As to your question of "Why can HTTP Debugger Pro see these requests": That's because it's not a proxy and is using a different technique (most likely API hooking) to capture requests. There are upsides and downsides to using such techniques.