When you log in to your account and arrive at the Tax Home, if your efiled Federal return still has a status of "pending" that is normal. For most people the IRS will not start processing returns until January 27, so most people who efile now will be in "pending" status and won't know anything further about the efile status until on or soon after January 27, except for a few returns that are pulled early for testing purposes. Once the IRS opens on Jan. 27, it generally takes 24-48 hours to hear if accepted or rejected, but there can be a backlog at first.
To check the efile status periodically you can log back into your Online TurboTax account and check the status at the Tax Home page. You should also get an email notice when the return is accepted or rejected. But as I said above, for most people that will be after January 27, unless drawn early.
You are correct that Florida does not have a state income tax. Only people who have Florida businesses or rental property with tangible personal property have to file a DR-405 with the county property appraiser by April 1.