I'm not entirely sure about the application bar (do you mean the panel, or when you go into the menu from the panel?). I generally use <alt-f2> then type in the command of the program.
For the *.exe question I should be able to shed some light. Many types of programs are executable, bash scripts, C/C++ binaries, perl scripts, etc. While there are some standards (bash scripts may end in .sh), there is no general rule that says a file has to be named with a certain extention. Files do contain properties and permissions, and one of those permissions is "executable." Enter a bash shell and type
# ls -al
This will give you a detailed list of all the files/folders in your default directory. Here is an example using mysql, in my /usr/bin directory.
-rwxr-xr-x 1 root bin 175196 2004-05-19 16:00 mysql*
See the x at the end of the first line? This stands for executable. Without this, a program cannot be executed. You can turn this on of off by using chmod
# chmod -x /usr/bin/mysql
The output would now be:
-rwxr-xr-- 1 root bin 175196 2004-05-19 16:00 mysql*
Now, I want that file executable so I'm putting it back with the +x option of chmod
# chmod +x /usr/bin/mysql
Not sure if that fully answered your question or not, but hope it helps.