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The photos seem low resolution. Maybe someone had old photos which they scanned? So it's difficult to say because we may not be looking at current photos. In general the photo of the engine compartment I can see the radiator support doesn't appear to have much rust/corrosion. Why look at that area? Because the paint on a radiator support isn't always that great for protecting against corrosion and short of removing the entire part (difficult) and either masking the stickers or replacing them it's difficult to clean an area like that without it being obvious. I know you wrote you can weld etc but you still need to know what you're getting into.
Inspect the vinyl top well and especially the lower edges near the trim. Rust can start there and it can be really difficult to deal with. I don't know the 1973 well enough to say for certain but to me the vinyl top molding does not look like the original factory style I was expecting to see.
Was the car stored inside or outside in the weather? I would inspect the trunk for signs of water (under the rear window and in what are called the "drop-offs" (area which extends down into the rear fenders from the main surface of the trunk). If you can inspect under the back seat it would be good as well. The rear seats bottoms of these old cars is actually pretty easy to remove. There is normally 1 "catch" or "hook" welded to the floor of the car and the seat has a wire cross member which is a bit spring-like. If you push on the front bottom of the seat while lifting they will normally pop-up. If everything else seems ok I would see if the seller would be ok with quickly removing the seat bottom. The carpet won't go all of the way under the seat and if the rear window is leaking the water will either show an issue under the rear seat or in the trunk.
I would also see if the seller has a lift so you can inspect underneath. Look at the frame around the body mounts. A frame can look good on the bottom and the sides but if the car spent a lot of time in a corrosive environment salt can sit of the top of the frame and cause damage. The mount areas sometimes act like traps or areas where salt and water will sit. Also take a look at the brake and fuel lines especially near any clamps.
Look at the dashboard near the base of the front window to see if you see any signs of corrosion because if you do the front glass may be leaking.
Inspect the CV joints on the axles for cracking. Also check the ball joint boots for the same. Keep in mind those things can be replaced but you need to know how much you will need to spend immediately. Someone should inspect the front steering components for you in general.
What are the white splotches on the trunk?
I don't understand your question about a flat tire. The tires are probably old and should be replaced for safety. A flat tire could simply be a troublesome valve stem schrader valve. It could also be a rim leak. It does look like one is flat and still being on the trailer I guess they filled it before they transported it so probably it's leaking to a point you could see it with a spray bottle of window cleaner (blue liquid). Just fill it and spray to find the leak. It could be someone ran over a nail or screw if the tires are new. Anyway tires should not stop you from buying a car.
It is easy to capture and place photos on this site. If you like the car though you need better photos and you need to see the car to inspect in-person.
Scott