Florence to Ravenna to Padua

Yes, possible. Trains seem fairly frequent taking 2 1/2-3 hours each. A rental car would be a pain with parking and ZTLs. A car service would be VERY expensive, since you'd basically be hiring it for a full day.

There are no direct trains from Florence SM Novella station to Ravenna so you’ll need to transfer at Bologna’s central station taking 2h 15m if you depart at 9:10a. The same with traveling from Ravenna to Pauda, you’ll need to connect on this route too. I see a train departing at 8:12p arriving in Padua at 10:27p. Trains leaving earlier take longer.
What are you doing with your luggage?

Possible but not enjoyable. Too much travel time. The mosaics are not to be missed and this is one of the few times I would recommend a one night stay. There’s no reason to take a tour of the mosaics. They can easily be seen and understood just using Rick’s book to guide you. Best mode of transportation is by train.

Possible but not very practical

It is manageable to see the main 6 or 7 mosaic sites (including St. Apollinare in Classe, outside Ravenna) on a day trip from Bologna. You'd only have time for a few of them if traveling all the way from Florence and continuing on to Padua. I wouldn't recommend it.

Will you have luggage with you? You will need to find luggage storage as well.