1.)
Yes, many airlines have currently suspended acceptance of pets as checked baggage. AA - the last of the large US airlines still accepting pets as checked baggage - stopped accepting them temporarily, and most European airlines who still accept them have suspended transatlantic flights. This will not change until pandemic-related travel restrictions are lifted, which will take several months at best.
Prices for pets as manifested cargo have skyrocketed together with general air cargo rates and now are firmly in the 'unaffordable' realm. Prepare to pay several thousand dollars for getting your animals to Europe especially if they have to travel in separate crates.
2.)
No, you cannot buy seats for pets, not on standard, scheduled flights with commercial airlines.
This would only be possible on a private charter - a thing that's cost-prohibitive for 99,999% of the general population for transatlantic flights.
3.)
Many - but not all - airlines do not allow carry-on pets on aircraft with lie-flat seats. This is a safety issue - lie-flat seats do not have underseat space where the carriers can be safely tucked away for take-off, landing and during turbulence.
Generally, your plan of taking the dogs in the cabin and checking the cats into the hold is a sound one, but there's caveats:
What breed are your cats? There are some breeds like Burmese or Persian cats that are snub-nosed/brachycephalic and on the ban list of most if not all airlines these days.These will not be accepted for travel in the hold as checked baggage.
Then there's your route. Between Orlando and Florence, one- or two-stop, one-airline flights simply do not exist. Changing airlines with all that entails (booking pets separately with each airline involved, retrieving them at the layover point and checking them in again) is something definitely not recommended for inexperienced travelers during pandemic times... and I`d rather drive to Miami than adding an additional stop somewhere.
What I would do: Fly
Iberia Miami-Madrid-Florence. This is the only one-airline, one-stop journey I could find currently allowing both carry-on pets and checked-baggage pets ,and allows cabin pets to travel in business class on the transatlantic sector.. If you are *really* lucky and your dogs as well as your cats are *really* small, you could even take all four of them into the cabin as Iberia is one of the very few airlines who allow multiple animals per carrier, provided the 8kg weight limit isn't exceeded.
You might have to plan the trip with a longer layover in Madrid so the animals can enter the EU there. I don't know if Florence qualifies as point of entry for animals from third countries.