Florence - Taxi Protocols

Yes. They take credit cards.
Yes, you can call a taxi for pick up or also use their app.
Technically hailing a taxi is not prohibited, but some of my friends who are taxi drivers in Florence told me that when they are on the road they are virtually always on the way to pick up a client (or have clients on board), therefore they cannot stop to pick you up. It's is not the standard practice for Italian taxi to just roam around hoping to be hailed. Gasoline is too expensive there. Their practice, after a client drop off, is to drive to the closest taxi stand and wait for the next dispatch. But in many cases, right after dropping off a client, they already have another dispatch to go to, so they don't sit idle for too long.

Also, if you call a taxi for pickup, the meter starts with the call so the taxi can arrive with several euro on the meter.

The two taxi cooperatives operating in Florence are below. You can call them at +39 055 4242 or +39 055 4390 to get a taxi or also use their apps (available for download in the respective websites below).
https://4242.it/en/
http://www.4390.it/en/

All taxi drivers are independent operators and owners of their taxi cabs (licenses cannot be awarded to companies by law). However taxi operators are partners in taxi cooperatives to share certain services (like radio dispatch, marketing, etc.).

Grazie Roberto and Frank -- such useful information!

I am now confident that I can make my way around Florence. I'm sure that for the most part I will be walking as it is not a large city - but at times, especially on the return trip at the end of the day I might surrender to a taxi.