How can I completely empty my trash? I mean how can I "securely" erase everything that is inside, in this way that it will not be recoverable any more!
Is it neccessary for a complete programm uninstall?
Presuming you are on OSX10.4 there is the option of empty trash or Secure empty Trash
And even more, go into Disk Utility and select erase, then erase free space. There is an option button for once over, 7 times over, and even 35 times over
Be aware that securely deleting mass amounts of data can take a LONG, LONG time. If you have more than a few gigabytes free and you choose the 35-pass secure erase free space, be prepared not to use your computer for most of the day.