Hi,
Yes, SUPEE-10415 needs to be installed for Magento CE 1.7.0.2 as well.
You can find the patch on the download page here: https://magento.com/tech-resources/download (go to "Release Archive" and scroll down to "Magento Open Source Patches - 1.x" where you will find the download for 1.7.0.2 in the dropdown).
All previous patches need to be applied as well.
As Magento CE 1.7.0.2 is compatible with PHP 5.3 I would assume the patch is compatible as well.
Anyway, I would recommend to update your PHP version as well. It is not safe to run PHP 5.3 since it does not get security fixes for over two years already. There is a special patch for PHP 5.4 support (at least).
