microsoft windows applications are not supported on os x?

[SilverTonguedDevil]

Wow! Many partial answers. Here is the whole deal....
-- The perfect solution is to find a "Mac" version of the software you need. That isn't always possible. The most popular apps, such as MS Office, Photoshop, Firefox, etc. are made for OS X, but plenty others are not. You could find a similar app instead--example: for Windows Movie Maker, use iMovie.
-- Mac OS is not Windows, so it only runs Mac applications ("application" is a synonym for "program").
-- To save yourself pulling out your hair, stop trying to download all these Windows installers / apps. None of them will ever work in OS X.
-- To use Windows apps... guess what? Install Windows. Two ways to do that...
(1) Use BootCamp to create a hybrid partition, buy a Windows DVD, and install Windows. (NOTE: This is NOT running Windows inside of OS X.) Then you can choose at startup to either start in OS X or in Windows. When in Windows, you can use Windows apps----unless they are only for XP or something old like that.
(2) Use a virtual machine, such as Parallels Desktop, VMWare Fusion, or VirtualBox. (NOTE: This IS running Windows inside of OS X.) The disadvantage is it doesn't fully control hardware in Windows, so it is not great for playing games.
-- WineBottler rarely works. It is an app that wraps a Windows app inside an OS X application bundle to facilitate launching the Windows app while using OS X, and without spending the money on a Windows install DVD. Oh, excitement! It's FREE! But like I said, only a few Windows apps really will work with it, so it is a real hit-and-miss thing.

Nit-picky definitions: For the most part, "executible" means anything that "runs" on a computer, so it doesn't have to have an EXE ending, just as a "movie" doesn't have to have the MOV ending. Without getting too geeky, executable, app, application, and program are synonyms--all the same idea.

"OS X Apps almost always end in ".dmg"
No, DMG is a type of image file that serves as a package for containment and security in transit (such as for downloading). It is similar to ISO, a way to put a group of files together--with the added advantage of compression. For Windows, the file that actually runs is always the one ending in EXE, but that could be how it is downloaded or it could be in an ISO or ZIP archive. When the EXE file is offered alone for downloading, it is more open to hacking in transit. An ISO or ZIP is better protection for a download, but we never have seen much effort to protect anything about Windows. OS X apps ends in .app, but that itself is a type of bundle, just as an exe file can be either a simple executable or a type of package (usually an installer) that has several files inside, including a simple executable. Inside any .app bundle is a MacOS directory with a simple UNIX executable inside. EXAMPLE: TextEdit.app has this pathway inside...
TextEdit.app/Contents/MacOS/TextEdit
The UNIX executable has no extension, so it is just "TextEdit". The other files in the .app bundle are used by the UNIX executable, such as resources and files that provide details for how it should appear or how the menus are arranged.