Transportation

You can take the Leonardo Express from FCO to Termini Station. Very convenient. Once at Termini, you can buy individual bus tickets or multi-day passes to get around on the bus system. See the ATAC site for info. Note that you must have a ticket when you get on the bus as they are not sold on the buses. The same tickets work for the Metro.

In Venice you will want a vaporetto pass. This is the "water bus" that locals use. Gondola rides are strictly entertainment/touring, not a commuting method.

I doubt there is a discount for Eurail pass holders.

I would like to suggest you pick up a good guidebook, like Rick Steves' Italy guide as he answers these types of questions and questions you do not even know you need to ask. He is great on the logistics of travel and specific cities (like where to find a laundry or a doctor) as well as sites and sights. Many books only cover tourist sights and Rick does a great job with the logistics as well.

Also, gondolas often go on the smaller side canals where vaporettos ( water buses, public transit) do not enter. At least our gondola ride did that with the gondolier singing, etc. No comparison between the two experiences.

The only significant non-train bonus associated with a rail pass for Italy is the coverage and discounts on international ferries. Nothing within a city. Trains and buses are generally operated by different companies with different tickets (with the exception of some railway-operated buses on the route from Venice to Austria). The local train from Fiumicino to central Rome is considered all first class, so only accepts first-class passes (https://www.ricksteves.com/travel-tips/transportation/trains/italy-rail-passes).

There are also buses from FCO to Termini Station. Most people prefer the faster Leonardo Express, especially after an overnight flight, but if you're in no hurry the bus is less expensive and imo takes a more interesting route. The airport bus companies are not part of the city bus network.

Some additional points about boats in Venice, the vaporetto boats are engine-powered, accomodate upwards of 100 people and run on regular schedules while the gondola boats are human powered, can accomodate only up to about 8-10 people and are usually private hire. The vaporetto boats operate on large canals while the gondola boats stick mainly to the smaller canals. It's worth taking one gondola ride, but you'll use a vaporetto for routine travel within Venice.

All Gondolas cost 80 Euro per boat, that's the official fare for a 30 minutes ride during the day.

Each Gondola can take up to 6 people, there may be Gondolas for 8/10 passengers, but I've never heard about it.

You are not forced to share a Gondola ride if you don't want to, of course you'll have to pay all the 80 Euro.

There are a few traghettos left for passengers crossing the Grand Canal at a certain spots, cost is 2 EUR per person. It is a large gondola with a rower in the front and back of the boat. Lasts about 5 minutes and the gondoliers don't sing or wear colorful uniforms. The cool people stand for the ride, but there are seats.

We visited Venice a few weeks ago. We had planned to have a ride in a gondola but, when we saw how busy the waterways are and watched a few couples being bounced around by passing water taxis, we decided to give it a miss. As another poster has said, some gondoliers will take to the quieter canals, but while you will get a more comfortable ride, I don't know if the route would be 'scenic'. Obviously, the quieter (ergo less popular) routes aren't going to pass by the iconic sights.