Self executable exes will run only if you install Wine first. This gives the
basic Windows compatibility layer to run exe files. If Wine is installed then
clicking on it will cause Wine to run the file.

As I said to Cori, you cannot just drag Windows folders from a Windows machine
and expect them to run in Linux. Most Windows programs store information in the
registry and have libraries in the Windows sub folders that make it impossible
to copy them even from one Windows machine to another. This is intentional to
prevent copyright infringement.

Linux does not work the same as Windows. Suffixes such as exe are meaningless
and for the most part you don't need to append a suffix in order for Linux to be
able to use it. For example, my_text_file.txt is the same to Linux as
my_text_file. Try this with Windows and it will not be able to use the file.

If you have Wine installed then you can right click and create a link as I
mentioned to her. In this case you should store them in their own folders in
your home folder.