Don't take the taxi. The spanish steps has a metro (submway) station right next to them. Take the train to Termini, go out towards the front of the station. I the lobby/ticketing area you will see an escalator down to the metro station. Us the self help ticketing machine (it can be set to english) and buy the full day Metro/Bus pass. (Costs 3.80 Euro).
Get a subway map too. Get on the subway that drops off at Spagna station (this is the spanish steps.) From the airport to the steps might take you 45 mins. Unless you miss a train at the airport and have to wait for the next one. You can then use the subway pass to get to the Vatican. Its a couple of stops out past Spagna. This would be the easiest and cheapest method in my book.
As far as how late you can stay, when you get to termini, check the train schedules to see when/if there is a last train out. You could even buy you ticket for it then so you don't have to worry about it getting sold out and so that you know what time you need to be back at the station.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013