Train Service

No, it is a continuously operating service. A train at least every 30 minutes and often every 15 minutes. There are no seat reservations or advance booking discounts.

No, it's definitely not necessary. This should provide the information you need - https://leonardo-express.com/en/en-leonardo-express-tickets/ . You can buy tickets when you arrive at the airport rail station, either from a staffed ticket office or from one of the automated kiosks. The kiosks are very easy to use, and have an English language option. The machine will provide a paper ticket, and you must validate the ticket in the machines near the train before boarding or you'll risk a hefty fine. This site shows what the validating machines look like - https://www.marthasitaly.com/articles/11/italy-travel-tip-validate-your-train-ticket .

As I recall, there are two Regionale trains that service the airport, so be sure to board the correct one. In addition to the Leonardo Express, the FL1 regional line runs from/to other Rome stations.

I agree that it's not necessary, but the lines for kiosks can be long. The bar (cafe) near the entrance to the trains sells tickets, something that many people don't know.

No
Purchase your ticket in the app once you are thru passport control
They can’t sell out, no seat reservations and price never changes

Ken, I am not sure your comments are currently accurate because of very recent changes. I thought I read (someone posted ?) that there is now a gate system where your ticket is "read" prior to boarding or entry via the gate to the train car. The days of the inspectors and fines are gone because you cannot get on without a valid ticket. Can someone else confirm this?

Frank,

From the Trenitalia website.....

"Single paper regional ticket
It can be purchased at station ticket offices, ticket machines, Territorial Points of Sale and authorised travel agencies. Single paper tickets must be validated before the departure of the train by means of the validating machines located at the station where the journey begins. Validation can take place until 11.59 p.m. on the day stated on the ticket itself. Once validated, the ticket is non-transferable."*. (I added the bold emphasis).

This explains all the options - https://www.trenitalia.com/en/information/travelling-on-regional-trains.html .

The gates are only at some stations, and are mostly so that they can keep some "undesireables" out. There are still ticket inspections on board the trains.