I WANT TO BUY PHOTOSHOP ELEMENTS BUT IT APPEARS ADOBE PRODUCTS ARE NOT COMPATIBLE WITH WINDOWS 8.
Where do you get that impression from? All current versions of Adobe products are compatible with Windows 8.
Windows 8 is listed in the Tech Specs
Internet Explorer 10 on Windows 8 comes with Flash Player preinstalled; you don't need to (and cannot) install Flash Player manually. Use Windows Update to obtain the latest Flash Player for IE10.