I'm thinking about switching from Android to Windows Phone 8. The only concern I have is whether I will be able to sync my email, contacts, calendar and tasks with my Google Apps Free Edition account (which sadly is not offered by Google anymore). ¿Is it possible or do I need Business Edition?
The feature you describe would be covered by "Google Sync" (their name for Exchange ActiveSync), which remains available to set up new Windows Phones with, until 31 July 2013 - it will also be available to set up new devices with after that date if you are a Google Apps for Business, Education, and Government customer.
The GDR2 update which is currently being pushed to devices has CalDAV and CardDAV support for google accounts. You will then be able to sync your account as soon as you get that update.