I would like to ask you, do the trash files gets deleted from the safe mode if I put them in the trash in the safe mode (but do not empty the trash) and empty the trash in the normal mode?
The safe-mode is only blocking certain features of Mac at the boot time. See http://support.apple.com/kb/HT1564?viewlocale=en_US&locale=en_US
It loads only required kernel extensions (some of the items in /System/Library/Extensions).
It disables all fonts other than those in /System/Library/Fonts (Mac OS X v10.4 or later).
It moves to the Trash all font caches normally stored in /Library/Caches/com.apple.ATS/(uid)/ , where (uid) is a user ID number such as 501 (Mac OS X v10.4 or later). It disables all startup items and login items (Mac OS X v10.4 or later).
Eg if you have a problem with a font, a corrupt driver/kernel, ... it's possible you wont be able to use your Mac, since the Mac can crash at boot etc, booting in Safe-mode is a chance to solve those problems.