You cannot transfer iPhone (iOS) apps to the Xperia (Android). They are different operating systems and android app will not work on iOs and vice versa.
I don't have the Xperia or an Android phone any more but they usually come with software (or software that can be downloaded) to connect the phone to the pc to transfer photos, music, etc. If you open iTunes on your PC is all of your music listed? If so all of the music should be in the iTunes folder in My Music.