1 & 3) I don't understand the need for a sim card - most places offer wifi which is more than enough to access your socials and emails. And it's highly unlikely you'll need to make calls or anything. That said you should be able to buy a sim card at the airport. Check the coverage maps for the various providers in Arg (Claro, movistar and Personal) and see if they have coverage there.

2) You will have to go through immigration (arriving from an intl flight), collect your bags and take them thru customs. Then you will need to check your bags in for the domestic leg of your trip. You'll be able to roam the public sector of EZE before going through security for your Eze to Cordoba flight.

I've had bank cards eaten by hungry ATM machines

Not in India anymore. You only scan, not insert your card.

An Australian Citibank debit card always worked for us and is a good deal, no fees for foreign ATM withdrawals or transaction fees (unlike the so called big 4 in Australia)...

If there's heaters in rooms then that's a bonus. I will be taking my own little blow heater anyway. I carted it around N/E India whilst travelling and it did a great job a few times of heating those rooms that needed it.

Beijing won't be disappearing so it'll just remain as one the places to go back to. In fact it's likely that I might get flights that connect through Beijing in the future so I can always make use of the long free visa that's available now. Northern china may be a place we head to when we have time in the summer rather than our usual winter escape.

We have our visas now so I can start booking things. I'll update when I get the ball rolling.
Thanks for everyone's input.

It's very easy to buy a sim card in Vietnam, very cheap for both phone calls and internet, no time limits except for some promotion packages. Simply stop by any retailers to buy a card and it takes you 30 seconds to top up by yourself

Good to have a budget, but keep in mind, its best too to have as much available funds at hand, even just on a debit card that you can use at ATMs.
I have got Nzd$118 in cash, and Aud$500 odd for 2 days in card, for my next upcoming NZ trip.
Hostels usually here in Aust, only accept overseas visitors, so they might or might not ask for a deposit on check in, I know a lot of hotels will ask for a card on checkin, some will take a $100/$150 deposit, which they say will be put back if you haven't used any phone calls, or minibars and don't have charge backs.
For Sydney, its best to get a Opal prepaid public transport card, though you will have to ask if they will refund you the unused portion at the end of 5 days.
Benefit of it is that if you use a lot of trips in a week, (I know yours is 5 days only), after a certain number of metro trips, you get cheaper prices, I think after 8 trips on the card, the rest is 50%.
Rather than Doyles, try the Asian eateries in Chinatown, or Cabramatta, if you want to have a look at Vietnam centric Sydney.
Lots of supermarkets around, and the eastern states ones also have things, like sushi prepared for sale, rare to see that in Adelaide supermarkets, (I do realise you are not coming this far south!).
Supermarket food is not all that bad here!
For $15 you can get a bowl of pho and a drink, for $20 you could add in some dim sims.
Bondi or Manly, a must for a look see, Bondi you can get a bus from the city centre, for Manly, use Opal ferry, (there is also the faster private ferry, I think this private ferry does not accept Opal).
Maybe $500 for 5 days in Sydney?
For FNQ, I would say, leave at least Aud$75, about $40 for nightly accommodation, the rest for food, if you can have a buffer of $100 a day on card even better.
I don't personally carry cash that much these days, as a lot of places in Aust will accept Visa or Mastercard (debit/credit versions), and less widely Amex.
Lots of places will not charge a fee for using cards, some places will.
For Sydney, on your first day, you might like to use the train, from the airport, yes this is a fast trip, but its all underground, so you don't get to see the scenery, and have to change trains somewhere, Central or Circular Quay, to get a bus/train to your friends place, if they are picking you up, all the better.
Have been to Sydney many times, but not to FNQ, only been as far as Brisbane.
Opal can be used on public transport (public ferries, trams, buses and trains), not sure about if they will refund unused Opal credit left on card though.

... I left with another prepaid sim card. This card is now expired. Neither place mentioned that I must cancel it there.

I purchased a China Unicom SIM card in Beijing on a pre-paid (for the first month) contract in Sept. 2017. The store rep told me to cancel it at the place of purchase before departure or there would be unspecified charges. I didn't do this and the card expired. I returned in June 2018 and went to the same store where I had to pay a fee of Y100 before a new card (and number) would be issued. I paid it and was told to cancel at the same store before departure or I would have to pay Y5 per month for the time that has passed if I return and try to buy yet another card. Morale for me: I've been informed/warned (and the penalty fee is subject to change).

Someone in a previous post on this topic suggested going to a ChinaMobile store and starting over. I wonder if this will work or is there a "national registry" of SIM card numbers regardless of company?

I got travelers cheques (in Euros) made for my travel in Europe in 2002. Didn’t end up using them, and then had them cashed in India in 2003. I can’t recall where I got them cashed but I had to pay for encashing them.

Have you considered putting some money on a Revolut card or two, and hiding those where you’d hide the travelers cheques instead? You’ll get better rates, and you can use the cards as normal debit / credit cards - will save you the hassle of getting travelers cheques made, or encashing them.