Transportation within Europe

I would start in Prague, work south to Italy and fly to Paris.

Only Euro carrier I have used is Alitalia to got to Athens, so no real background on other Euro carriers. Alitatlia was fine ( 2014)

a. Order of destinations and transportation to/from each locale.
Prague to Ljubljana to Tuscany (you have to research what city in Tuscany you want to stay in).
Then fly from Florence to Paris.

b. What inter-European airlines have you used or recommend?
Several but the brand does not matter;
you just want to only buy direct flights since these are short flights

c. Would night trains be feasible to travel from one place to another?
No. But if you go from Prague to Slovenia (Ljubljana) by train you may want to stop in Vienna to break up the lenght of the train ride by staying overnight in Vienna

Many/most of us are sleep-deprived and jetlagged on the day we arrive in Europe, so we don't expect to get much real sightseeing done that day, just wandering around outdoors attempting to stay awake. Keep that in mind when deciding how many nights to spend at your first stop. I would definitely skip Prague if the alternative was to fly there from the US, spend only two nights in the city (giving me just one usable day), and then have to slog all the way to Ljubljana, which is at least 10 hours away by train and without a real night-train option. (I'd consider Zagreb instead, because it's only a bit over two hours from Ljubljana and a full day plus some wandering hours would be a reasonable time allotment for that city.)

I suggest checking airfares before getting wedded to a detailed schedule. There are sometimes differences of many hundreds of dollars when you look at flight destinations that aren't terribly far apart. Better to see what's out there before you get too deeply into your planning.

Your itinerary starting in Prague is just not very efficient. Those Alps are difficult to cross.
I would suggest substituting Budapest as you can much easier get to Slovenia from there. We have been to both cities and Budapest is much cheaper and we really like the young folks there.
You can pick up and drop your rental car in Slovenia and catch a bus over to the Trieste./Venice area where you can catch a train into Florence. You can rent a car in a Florence city center location as you leave town. Most of the hilltowns of Tuscany are just an hour or so south of Florence, and virtually every farm has apartments and rooms for rent.
You can go to Wikipedia and look up airports to see which budget airlines in Italy can get you to Paris. Many people fly in and out of Pisa Airport to other places on the continent, and it is a 1 hr. local train ride from Florence. We usually fly EasyJet.

Prices and schedule of flights determine my choices, not airlines. Use Skyscanner to choose flights.

Have flown Ryan (once), EasyJet (twice), Vueling (once, about 10 years ago) -- all were cheap, short flights, went as expected. As Suki noted, choose based on schedules, prices, ease and cost of getting to/from airports.

From Prague, it's possible to take a direct night train to either Budapest or Vienna. From Prague to Ljubljana, an overnight plan requires a connection in Munich at 23:30. There's also a night train from Vienna to Florence and, if departing Ljubljana, you could connect to this one at Villach about 1:00 a.m. (allowing maximum 5 hours to sleep).

Looking Up Train Schedules and Routes Online gives you the Deutsche Bahn train schedule link and tips for using it.

Thank you all for taking the time to give great detailed information. You have given us a lot to think about.

Skyscanner.com has several helpful features. It specializes in the budget airlines that are so popular in Europe and that price their flights on one-way tickets. It allows you to type in a departure city and then see all the airports in your desired country. And it does not sell tickets, instead linking to the airlines' sites.

Or you can read www.seat61.com for rail travel.