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That resistor is called a wirewound or power resistor. 5 Watt size. I've seen them charred and still work, that is why they are made that way. One reason I like military electronics. Designed to be repaired.

The capacitor is failed and is probably failed with some DC resistance, causing the wire-wound resistor to see greater current which is heating the resistor. It should be fine but a quick test would be a good thing. You might have to remove it from the circuit, just one leg is fine. It is a...

Yes, the transducer is shot. Running it open (without a resistive load) can cause this. Reasonable cost? Not likely. A 0-200 microampere 55-65 Hz transducer isn't a standard item. TransData makes a 55-65 Hz, 1 milliampere unit which you could use, employing a current dividing network to...

Higher frequency isn't an issue. The problem is lower frequency since the exciter current will be low, causing the voltage regulator to peg. Running the output transistor(s) at maximum causes the issues. The engines can take the abuse. Just don't shut down immediately after hard use, let the...

Yes, always leave throttle (governor speed control) at 60 Hz. The voltage regulator lasts longer that way. The basic Kill-O-Watt meters work well enough and are somewhat immune to back EMF (reactive current) which throws off meters. Using utility current to calibrate the transducer and...

Digital meters can be picky, they read fine without a load but put anything other than pure resistive on them and they don't seem to deal with the back EMF. The adjusting screw is the bias screw, it should only be moved with known frequency. It affects the entire scale. Basically, the...