No need to root your phone. You just have to have the specific folder for each type of sound.
Go to "Menu",click on "My files", and within the sdcard, create a folder named "Sounds"
/sdcard/Sounds
1. For Alarms, create a folder named "Alarms" within that directory. Copy/move here the sounds you want as your alarm.
2. Likewise for Ringtones, create a folder named 'Ringtones", and copy/move here your preferred music
3. Lastly, for Notifications, create a folder named "Notifications", and copy/move here your preferred notification sound
So, basically, within your sdcard, you have these directories:
sdcard/Sounds/Alarms
sdcard/Sounds/Ringtones
sdcard/Sounds/Notifications
When you choose ringtone for phone/notifications in your Settings, the music you included in those directories should appear.
For Alarms, go to Clock, Add alarm, and then there's an option to change the alarm Ringtone there.