I want to get a call from somebody and after talking with him redirect that person to another number, on my charge, like call-centers do. Is that possible and if that's so, there is any application that can do that?
I guess you could do this using the "Conference Call" trick on android (natively!).
The screenshots below are for vanilla froyo and may vary with your version/dialer app.
During your call (Don't hang up the call), after talking to that person, press the "Menu" button on your android. Press "Add Call" from the menu.
Dial and call the number you wish to "redirect" for him. (on your charge! (which is what you asked for right?) Means you will loose money for this call as if you are calling it)
Now press menu button again when call connects. Press on "merge call".
Finally, Press the menu button again and click on "mute" to make them think you have terminated your call. (you mute yourself but you can hear the conversation between him and the "redirected" call)
Remember, while doing these, you will be charged for 2 calls simultaneously!
The feature you're looking for is known as call transfer. It's pretty common on office PBX and VoIP systems, but is virtually never seen with mobile phones. The existence of such a feature would require some intelligence in both the device and cooperation from the carrier's equipment, both of which are generally absent. As far as I know, there is nothing in the Android source code to support this feature.
In short, no, it's not really possible.
While it may not be exactly what you're looking forward to, Google Voice has something like this.
If a caller calls your google voice number, all the phone you have registered ring at once. So you pick up the call on your home phone, then decide you want to go out. Google Voice lets you press 4, and it starts ringing the other phones again (without the other caller hearing anything). All you do is pick up the cell phone, and your call is transferred seamlessly.
I only post this in case someone is looking for this specific solution. Otherwise, you'll have to host your own PBX (like Asterisk) and set it up yourself. Android (well, specifically the cell carrier) doesn't have this option.