Don't forget you have "float level" and "float drop". When you have too much float drop, like yours, the float can stick on the bottom causing the carb to flood.
Yes, welcome. Do not start your life with an old car replacing parts just because they are old. Old cars can be very simple and reliable. You are in the right place. You will get a little education. Your solution will probably be simple.
While idling put hand over carb opening- choke it. Does the engine speed up? This would indicate a lean condition, a carb problem/vacuum leak. Take a compression test. Tight valves?
That looks like the old vacuum fitting that goes to the brake booster. Your car has seen many modifications over the years and it will take a while to sort it out. You have come to the right place.
#1 looks to me like it is over-heating. Since in the beginning there is some inconsistencies in the readings ,I would try another brand of plug and see if that continues.
How old are the ignition wires? I have seen wires that will occasionally arc even though they ohm out OK. This is due a breakdown in the insulation by antifreeze soaking. Try looking at your motor running at night to see it.
If your motor dies when you install your air cleaner- there is something wrong with your air cleaner! Or- the A/C stud is pulling and warping something.