exe files won't open after downloaded from Safari on my Mac OS X 10.4.11

They're not supposed to, unless you're using software such as Virtual PC or the Q emulator to run Windows, or they're self-extracting zips, in which case StuffIt Expander will open them.

(98186)

I use the free Unarchiver: http://unarchiver.c3.cx/unarchiver

I have just tested it on a self-extracting Windows Internet Explorer and it opened it first time on my Mac.

However, as you have been told, normally Windows executable files cannot be opened or used on Macs.