How easy and safe is to Uber in Rome and Florence? Are there better alternatives? How easy is to get a regular taxi service?
Standard Uber is illegal in Italy. Only Uber black working and probably more expensive than local solution.
Taxies are linked to central despatching offices and can be summoned by phone. Number of taxi licenses is controlled and kept a bit too low, so in some situations (big tourist numbers, an important event in town, bad weather) it may be difficult to get a taxi, you have to keep trying.
I don't think Uber operates in Italy. Taxis are easy and fairly inexpensive. Not cheap but fair priced. You must get your taxi at a taxi stand since you cannot catch a taxis on the street as you would in Chicago or New York. All are metered with a cc machine. BUT --- always smart to make sure before getting in that the machine is "working." Our experience in Rome has always been positive with taxis. If you order a taxi the meter starts when they answer the call so it may arrive with a couple of euro on the meter. Not a rip off or a scam.
You can see where Uber operates worldwide on their website. https://www.uber.com/us/en/r/cities/
Good info on taxis and clarification on uber in Italy
https://community.ricksteves.com/travel-forum/italy/taxi-drivers-88a2c187-461f-4cb9-935d-8599a564171e
My recent experience with taxis and uber black is that taxis are less expensive.