Does Syria have a federal government?

No, everything is centralized under the president. Governors in Syrian provinces are not elected by the people, they're appointed by Bashar al-Assad himself. All of Syria's provincial governors are associates and henchmen of Bashar al-Assad.

As for Syria to get a federal government, that would be a great idea once Bashar al-Assad falls from power, since Syria has many multi-religious and multi-ethnic communities.