No issues with Customs.
BUT you have to pass through French immigration to leave the airport (typically 1 hour). And you need to allow enough time to pass back through security and get to the departure gate (typically 2 hours).
And it is an hour each way between the airport and central Paris.
Unless you plan to transport goods deemed undesirable for entry to France, customs won't be fussed about whether or not you decide to visit Paris from CDG. For most people, customs will mean a walk through the green Nothing to Declare channel.
Immigration staff, on the other other hand, very likely won't be overly concerned either. If you hold a US passport, tell the agent at border control you want to go to the city centre for a few hours and will return later that day to travel on to Rome. You'll be stamped in to the Schengen zone and after that it will be a matter of ensuring you return to the airport in good time before the flight to Rome.
If your bags will be checked through to Rome and you'll have a carry on bag you'll have to deal with it unless you want to take it with you to the city centre. Bagages du Monde operate left luggage at CDG: www.bagagesdumonde.com/en/left-luggage/offer
With time needed for immigration, (potentially) left luggage drop and collection, the journeys to and from the city centre and lead time before the flight to FCO, your eight to 12 hours may be five or six of real time available.
This question crops up quite a bit on the Paris forum, so you may get some ideas there regarding the logistics involved. Here's a thread to get you started (but there are many others, try searching the forum!) - it kicks in with good info on the second page regarding timings and so forth.
If you're heading back to the US from CDG, you may need to allow a little more time to get through security. But with eight to twelve hours, a quick nip into Paris certainly should be manageable (I'd do it, that's for sure!).
Whether or not you leave the airport, you will go through Immigration (Passport Control) in Paris, as it is your first port in the Schengen area.
As I understand it, OP's trip is from Rome to Paris to Newark. If that is correct, much of #1, #2 and #4 is wrong and/or irrelevant. Arriving in Paris from Rome, there will be no immigration, no customs, no passport control, and no border control. Or, sorry if I misunderstand OP's travel plans.
#5 is right. If it is indeed Rome TO Newark travel, the Rome to Paris segment is a domestic flight for all OP's purposes. Their only border control will be the exit control when leaving Schengen before boarding the Paris to Newark flight.
If "8 to 12 hours" means a choice between different flights, I would personally opt for 12 hours, which would allow 6-7 hours in Paris proper.