This question and ones like it are asked often. Please read the "Guide to Trains in Italy post at the beginning of this section.
The train station is in the city center and you will need to either take a Taxi or use the port shuttle to take you out of the port and then grab the number 1 bus to the train station or grab a taxi or walk (about a 1 mile) but you can read details in the train post.
If you had, you would have seen this article - Livorno and Florence in which both of your questions are answered- The trains schedule says Depature from Livorno to Arrival in Firenze SMN (The correct station in Florence) is roughly an hour and a half trip.
I suggest you read the article and look at the map provided. Having a good Florence tourist map (search Amazon or go to a book store) before you go would be wise too. If you have not been there, its not obvious where to go (most of the sites are walkable if you don't mind putting in a couple of miles on foot.)
As Jim C has stated, Florence is very walkable. A good map is important so that you can plan ahead where you intend to go (and then follow the plan.)
Florence, like almost all Italian cities and towns, is not laid out on a grid like most in the US. Streets tend to veer off at funny angles without being really noticeable. It is very easy to get off course.
Radiance of the Seas - Nov 2006
Legend of the Seas - Jun 2007
Costa Fortuna - Mar 2008
Legend of the Seas - Oct 2008
Celebrity Constellation - July 2009
MSC Orchestra - Jan 2009
Navigator of the Seas - March 2009
MSC Poesia - November 2009
Jewel of the Seas - June 2010