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You don't need to worry, the battery or the phone will not take damage by overnight charging/longer charging times.
As you can see at the following link under the headline "Improving battery performance", it's recommended to charge your device often:
http://userguide.sonymobile.com/referrer.php?region=global-en&product=xperia-c#Battery.html
No, it won't damage your phone
does the battery won't be damaged too?
You don't need to worry, the battery or the phone will not take damage by overnight charging/longer charging times.
As you can see at the following link under the headline "Improving battery performance", it's recommended to charge your device often:
http://userguide.sonymobile.com/referrer.php?region=global-en&product=xperia-c#Battery.html