When you get the new wafer thermostat, hold it up to your ear and gently shake it so you can hear what a good one sounds like. The new switch may have a strip of metal across the bottom that the old one doesn't have. It wouldn't fit in my holder so I took the metal strip off.
For the motor, maybe try some electrical contact cleaner.
Humidity - I have 4 of the Incutherm thermometer/hygrometers and they all read different and none of them are accurate. I bought a wet-bulb thermometer to hang in the window of the door.
https://www.amazon.com/Taylor-Preci...-Precision-Permacolor-Mercury-Free-Hygrometer
Not sure about the temperature alarm. Can't tell from the photo but it is a low voltage buzzer and could be wired off the toggle switch. You'll have to open the electrical box to see how it's wired. It makes me wonder if the bulb holder on the left is a temperature controlled contact that completed the buzzer circuit.
On my 2nd incubator all the hardware was rusted or tarnished badly. Since the sizes were different from what is currently available, I ran them through my reloading tumbler to clean them up. I then painted them with a spray metallic paint.
None of the redwood incubators I have seen have been painted in the inside. To seal the interior defeats the purpose of the redwood. When you run it, you'll want to run it for a couple days at high humidity so the wood absorbs some moisture, then drop the humidity down before putting in your eggs. It might be whitewash instead of paint. If it is paint, you can bet that it's lead based.
The exterior finish on my Leahy was in good shape. I just cleaned it with some Murphys. The second one needed a total strip job. I finished it with a couple of coats of Danish Oil. I bought a jar of Kramer's Best Antique Improver to coat the Leahy with but just haven't done it yet. I did use it on some antique picture frames and it did an amazing job of restoring them.
The switches on the front are Despard style. You can buy the switches and plates on Amazon. Not sure about the indicator light. Mine just has a red light the same size as the switches. You'll have to pull the switch plate off to see what's inside.
I would recommend adding a fuse to the electrical box if you have room in the box for it.
https://www.amazon.com/gp/product/B005T6O72M/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1 A surge protector alone doesn't do what a fuse will do. A friend made a homemade incubator from a wine chiller and it caught on fire from an electrical overload.
Reading back on your earlier post, one switch powers the light, the other switch powers the heater and fan. That switch stays on unless you open the door. Turn it off or you blow hot air out the door. The indicator light only comes on when the heating element is heating. The fan runs continuously and the heating element & indicator light is wired through the wafer switch.
There's not a photo of the thermometers. Is the broken tube above the water tray? If so, GQF sells a wet-bulb thermometer that is a metal dial type but the bulb sock goes into the water tray.
My water tray was gone, I use a deep lasagna pan and cover it with foil to regulate the humidity. It was trial and error to figure out how much to leave open. I put a ping pong ball in the pan to keep the foil up off the surface of the water.
Hope this helps. You're going to love it once you get it running. I wouldn't trade mine for 2 modern cabinets.