Does wi-fi sleep policy "never" mean that my phone's battery will be drain a lot faster? I have just decided to change my settings on the wi-fi, because it seems to give me a hard time regarding the fact that the some application are "unable to connect to server".  However, I am worried about the battery life. Does the setting "never" mean that the phone will scan non-stop, draining my batter like crazy?
If you have "wifi-sleep" on, when the device goes to sleep, the wifi connection will disconnect from the access point. It doesn't happen right as the device goes to sleep, but a little delay after. It shouldn't drain the battery much more then just having wifi on. 

Of course, if you have very network active apps running, then it may drain it a bit more. But on the other side, if wifi goes to sleep, and you have network active apps, they will just use your mobile connection, if it is available.