Taxi from central Roma to FCO is about €45-48.

Don't know about taxi fares in Firenze.

Taxi Florence-FLR. 6 miles, 15 minutes. 22 euro 1euro supplement 1 euro/bag.

From the Pantheon you can always take the tram from Lago Argenina to Tastevere train station then take a local train to the airport. This is very direct and costs less than €15. We have taken this route several times with no difficulty. What time is your flight?

Our flight is 1:45 in the afternoon.

You definitely have time to take the local train from Trastevere. It's an easy safe ride and you'll be traveling with more Italians than tourists.

For traveling "inside of Florence," there are only a couple of minibuses that go through the historic center. Otherwise, you'll be walking everywhere. The only bus I took in Florence is the one up to Fiesole (highly recommended). So, you don't need a bus app for Florence, unless you're staying outside the historic center.

Can I assume that it is easy to buy a bus pass at the airport in Florence?

Again, you don't need a "bus pass" for Florence. If you're taking the bus in from the airport, just buy that single ticket. When you go to Fiesole, just buy two local bus tickets (different tickets than the one for the airport bus). You will most likely not be taking any other buses while in Florence.

Alternatively, you could take a taxi from the Pantheon neighborhood to Termini (about 10 euro), then take the Leonardo express train from Termini to FCO (about 14 euro). I returned to the airport that way last month; it was simple and worked well for me.