That's not even a honorable mention for a Darwin award. Lights were on, but no one was home applies maybe...

I wouldn't expect it runs since there's no head bolts on it?

If, as you say, "most" of the body mounts are "rotted", your car may have serious structural issues. Replacing the rubber won't correct that. Depending how bad, it may not be safe to drive as is.
Properly repairing the under structure and pan metal is not a buy parts, bolt in, type of fix. It's a large commitment of hours of skilled body work. Not to scare but be aware.

Well, if I hadn't gone out and taken picture for this one, I might agree, Joe.
No good deed goes unpunished as they say. I'll be silent from now on.

This started off as a radiator core question and look were it's gone.
This seems to be a common issue because people believe thermostat "controls" engine temperature to the temperature on the package. I've posted on this subject before, it doesn't work that way, folks! Also, lower wall temperature affects combustion and can causes other issues; power, lube, sooting, tolerances, emissions, etc.
Actually, higher coolant temp will dump more heat out the radiator, so it's counter intuitive as well. {It's an easy calculation if you know heat transfer.}

You'll probably have better luck finding a replacement. There's jukebox restoration places, not this forum.

My, my, my. I think awhile ago the Kanter's posted a big show about how great a cure this was for them.
Don't mess around with brake systems. Do what it calls for.
Your life and guy in fronts is at stake when you press that pedal. Sez biased old guy... Frankly, I'd get rid of it and put a modern dual system in with the money to repair it. Like I say, if they were any good, they'd still be using them.

You can pull the cover off the side and expose the valve train and see if they are working or not/where you adjust.
The intake would have to be partly plugged, if not getting fuel mix, if that's operating Ok. Mice make strange stoppers. A bore scope or fish a wire may lead to clues. I use a blow gun with a plastic tubing in place of the nozzle and fish it in places and see what comes out. Compression test is another easy option. (Don't ask me how I had acorn shells in #8 and the plug was in.) I always check for that stuff before I fire up. Prevents damage. Too much emphasis on getting them running "right away", but not right way to go...
I don't recommend you mystery oil down through your carb. Add to gas or the crank case, but what are you doing it for if it's a mystery and you don't know what's wrong? Do you really need it or just because every else does it?
If they're firing but not burning, the exhaust manifold won't get as hot there, so an exhaust thermal scan would provide clues. Those are pretty cheap at the chinese takeout now. All this could have been prevented with a systems approach.
I bet it's something else.

Things must be heating up. A few years ago my whole running engine was estimated worth $500 on here, so maybe I better sell manifolds???

What I run into is either buy repro, have none, or more costly and iffy rebuilts/used when OEM no longer.
So as much as we hate/chastise the repro guys, without them we may not have parts at all. Only going to get tighter down the line.
Burn up the phone line, not the forums, if you're not satisfied. I see this going on all over, they all take it on line, everyone chimes in, and nothing happens. Why? It's easy.
I have a whole tray of new Cu washers from back in the day, so
like the boyscouts, be prepared...