Can I download music from itunes web site without itunes software? [duplicate]

Currently, iTunes will not work, not properly at least, with Wine or Playonlinux or Crossover (it used to work a while ago). What will work, though, is to install Windows in VirtualBox, and install iTunes on top of that installation. This is a bit of an overkill for iTunes, but if you have Windows installed in a vbox anyways then it does not cost you too much trouble.

iTunes is absolutely required to access iTunes if you want to buy music. No alternatives exist. However, as I was informed in a comment -- other software exists to access free contents.

For some type of the media, there are alternatives to iTunes. For example, you can buy music from Ubuntu One music store or Amazon. I am well aware that this will not replace iTunes Music Store, but you can get music from the Big Four in these stores as well.