Access CiviCRM fields from Drupal entity
The website is a separate entity from the contact; so is the address data, though some of it is made available (for the primary address only) on the Contact entity.

I know the Address entity is available; I don't think the Website entity is, but that's out of an abundance of caution; it's basically identical to the Phone entity, so you should just be able to edit civicrm_entity.module to patch it in.  If you use it and it works, don't forget to submit a patch upstream!