If you do not take a flight, the actual fare is lost, but taxes and airport/security fees are refunded to the payment method used. This takes a few days, though. The ticket status on CheckMyTrip (requires booking reference and last name) will likely update quicker.

It really depends on the ticketing agent -- basically the Amadeus system is a piece of really arcane technology that is difficult to use, but gives full flexibility in booking, while airline websites go for simplicity and will not even present you simple options like "extend this layover by 24 hours, but keep all the flights on a single ticket." So a skilled agent can definitely get you tickets that are not available online. Airlines use Amadeus even to sell their own tickets, so airline agents have access to the same ticketing options, but often it is a skill issue.

And more specifically, being in a long-distance relationship with a green card holder is a strong indication of immigrant intent.

You can't do this while booking online, but it is perfectly valid to create a single ticket with a layover of more than 24 hours, taking the onward flight a day later. It's also usually possible on such a ticket to check in your luggage to the final destination, as many airports start accepting luggage on the day before the flight to allow passengers to come to the airport by public transport with only hand luggage on the day of the flight.

So: all tickets start out as unpaid reservations. There is no way to not hand out reservations. On the other hand, immigration officers can verify whether the ticket status is "confirmed", so a pure reservation will not serve as a proof of onward travel.

This is the way the system works: first a reservation is created, which fixes the itinerary and price, and then payment is processed, which in several systems is not instantaneous, so the ticket can be held in "reserved" state for several days. Usually, it's the half hour between you selecting your seat and finally entering your credit card information after unselecting all the upselling options -- during this time, your ticket existing already excludes other people from selecting the same seat, so there is never a case where you make payment and your seat is gone.

There are some rare political constructs where a country issues a passport for someone who is not a citizen of that country.

Yes, 8 hours is fine on all but low cost carriers. I've sometimes dropped off checked luggage a day early, which makes getting to the airport easier on the next day.

The last time I was there, rather few places accepted Visa (only the ATM at 7-11), and I had more luck with MasterCard.

The Amadeus system works precisely by locking the fare and then giving you (IIRC) 48 hours to make a payment or cancel. The travel agency I normally use uses this to prepare the ticket according to my specifications, send me the booking reference which I then verify on CheckMyTrip that it is indeed what I want, and then when I confirm, my credit card is charged and the ticket becomes valid. Charging for this is a complete dick move.

@akshayub, I booked it this way -- travel agents can build tickets like this in Amadeus, but it requires a few extra steps because it's not in the search results.

I've even done this intentionally -- booked a ticket that would have had a two hour connection and extended that to 26 hours by selecting the same flight number one day later for the second leg. This works best with airlines that permit check-in on the previous day, while budget airlines might get confused.

The immunity isn't provided by the antibodies, but by the mechanism producing them on-demand. You would normally have rather low levels unless you have had recent exposure to either the virus or a vaccine, so any recent test showing high levels would be grounds for a quarantine order without a vaccine certificate explaining it.