How to Erase files COMPLETELY???

In the Finder menu, when something's in the Trash, you have the option of Secure Empty Trash. As far as other temp files that could be slowing down the system, you can empty those by starting up in safe boot, logging in, and emptying trash, then restarting. If the computer is still slow afterwards you'll need to consider what background processes you have running in Activity Monitor and if something is set to automatically launch after login, specifically your Login Items in System Preferences->Accounts.

 

Deleting an application for example from Trash fails to get rid of .plist and certain other related files. I now use a third party application to completely remove all files associated with an application.

I prefer CleanApp, but AppZapper does similar. [There's another one called PermanentEraser, but it's scary because it doesn't have prefs you can set, it just deletes everything that's in the Trash - poof!]

I'd also suggest cleaning your OS with OnyX, a free maintenance utility from http://www.titanium.free.fr/pgs2/english/download.html