Can I backup using Time Machine and restore to another account? I am planning to re-install the OSX when Mavericks release. I am also actually planning to change my username after re-installation.

I need to backup my whole personal folder under username "a", but if I changed my username to "b", Can I still be restoring my personal data to "b"?

I know generally there is no problem for this, but I am wondering if iTunes library still recognise my new username and locate my every music file location?
You cannot directly restore to another account from Time Machine, but you can rename the user after the restore. After the fresh installation of OS X, restore the data and then do the user rename.

Follow the process outlined in Changing user account short name to rename your user "a" to user "b".