Heathrow to Norwich

Either-
National Express bus, broadly every 2 hours to Norwich, journey time about 4:20;

https://book.nationalexpress.com/

(or, with contactless, at the ticket machines at Heathrow)

OR-

Elizabeth Line to Liverpool Street (pay on the day with contactless)- 1 hour journey time
THEN
Greater Anglia Trains Liverpool Street to Norwich 1:45 journey time every 30 minutes, so end to end journey say 3:15, 1 hour faster than the bus
- pay by contactless at the station. You can buy much cheaper train specific Advance fares online- but that is playing roulette with your flight being on time, and the time immigration takes.

So for the first train on Elizabeth line to Liverpool Street Station, can I buy it online as a mobile ticket or must I get it at a ticket machine?

There are no actual "tickets" on the Elizabeth line for a single trip. You just tap in and out with your contactless payment. You must use the same payment method for both taps.

I have three contactless credit cards I always use in Europe, a couple of MasterCards by Synchrony and Citibank and a chase Visa an US Bank Visa. I have read on TFL website that some contactless cards issued outside of the UK do not work. How likely is it my cards wipold not be accepted by TFL when they work everywhere else without any problem?

Very unlikely that none of your cards will work.

Also it is not true, as stated above, that

There are no actual "tickets" on the Elizabeth line for a single trip.

Many people use contactless as stated, but there are also ticket machines at all the Heathrow Stations where you can purchase actual physical tickets. Those machines are National Rail, not TfL machines. So the alleged issue with TfL does not apply.

Lastly, although it will cost you £2.50 more (£15.80 rather than £13.30) you can buy tickets for the Elizabeth Line journey at any National Rail website/app either before you arrive, or as you land at Heathrow.

Further additionally (good to know if the Elizabeth Line is having problems on the day) it is possible to get to Liverpool Street by tube from Heathrow (and takes just 10 to 15 minutes longer). There are various ways to do that, and that option costs £5.60.

Although I am pretty certain that the Elizabeth Line ticket machines also take cash as well as cards I know that the tube machines do. And the prudent traveller always travels with some cash with them.

It's also possible to buy a ticket at Heathrow (or online beforehand) through to Norwich using the Elizabeth Line route. But that will be more expensive than using contactless on the Elizabeth Line and a ticket from Liverpool St.

Tank you all.