How long to get into Rome from FCO?

Probably not. FCO is about 45 minutes outside of the city by taxi, maybe 50 minutes by train. One can never predict how long it takes to get through passport control. And, will the plane even arrive on time? And how long will it take just to get off the plane? Have a great trip.

Welcome

I wouldn’t risk it if it costs $$
Flights are often delayed, passport control can take time
Then you need to figure about 45 min to your hotel and then get to your meeting spot.

Taking an important tour in a jet lagged state would not be my choice

Very doubtful, if not impossible. It often takes us a long time to simply get through immigration at FCO at that hour because so many flights from the US arrive at that time.
How were you planning to get to your hotel…have you scheduled a private transfer directly to your hotel?
Is it possible to schedule the tour at a later time?

You will very likely miss it. The Rome airport line to pick up a taxi when I was there in May was ridiculously long. I had planned to take the Leonardo Express train (do the non-stop one) into Roma Termini anyway. And it was very crowded. I had the Trenitalia app to buy my ticket, but others were waiting in a line to buy tickets. That process is slow because people aren’t familiar with the ticket machine, etc.

On a different leg of that trip, I caught a taxi from Roma Termini to go to my hotel near the Pantheon. Traffic was thick, and it took much longer than I expected. The driver was very pleasant, though, so I could practice my Italian. : )

Don't even consider it. You couldn't do it even if very lucky. Even if you land early our experience (multi-times) with immigration is 30/45 minutes till over three hours. Depends on staff on hand the number of plane at or nearly the same time. You land at 8, off the plane in 10 minutes, clean immigration in 30, no checked luggage, and you are at the train station in ten more minutes -- it it now 8.55. buy your ticket in five minutes - no line - and now you have to wait for the 9.10 train., You on -- opps forgot to validate tickets and they hit you with a 50 euro fine but you are still moving to the station. (there is a new system so validation may not be required). You arrive at Termini 35 minutes latter - 9.45 but historically the LE uses platform 25 with long, ten minutes, hike to the front of the station. It is now 9.55. Don't think you are going to make it.

We fly into FCO airport at 8:05 ......Can we make a tour by 10am that is 15 mins away from hotel?

Only if you can make use of a Transporter system as used on Star Trek, and can 'beam' yourself from place to place.

My next best answer is ' only if the 10 AM tour is the next day'

That feels very dicey. We waited in the Passport Control line for a full hour after landing. It may be lightning quick when you come but you just can’t be sure.

Its much quicker at the airport if you have an EU passport. I am on the train to termini and at termini very quickly with my Italian passport and I don't think I could do what you are considering. The non EU line in the mornings when several planes land from the USA is VERY long for passport control.

We are flying Icelandair from Seattle to FCO, stopping in Keflavik to change planes. I believe we clear passport control into the Schengen zone in Keflavik, so can skip the passport lines when we arrive at FCO. I think we will still need to go through the customs line when we arrive at FCO after we collect our luggage. Is that correct? Thanks!

If you enter the Schengen zone somewhere else, there will be no passport control in Rome. Customs is just a walk through the "Nothing to declare line". The Customs officer may check people at random but I've never been stopped in over 40-50 trips.

It is very unlikely a person can make a tour in the city 2 hours after landing, even if coming from the Schengen zone. From the time of landing to the time you are in a hotel in the city center, one hour is not enough.