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Rooting means gaining access to remove or change/edit system applications. You need to check XDA forum for that,there are individual developers.
Rooting is a name given to allow you access to the root of your device which will allow you to do what Alex said as well as lots of other things - Just be carefull that in doing so depending on how you root you may loose your DRM keys as there is two types of rooting full root and partial root, Full root requires your bootloader to be unlocked which is how you would loose your DRM keys
It is not sure if you will/will not,this has to be checked with your local sony team:
http://www.sonymobile.com/global-en/support/contact-us/
Unlocking bootloader will void warranty.
Depends how you do it