...Is there some rule of thumb of what is prudent?...
The motor is not the only thing drawing amps. Your servos also draws amps. A typical 9g servo, when stalled out, will draw approximately 3/4 of an amp. In other words 4 servos will draw about 3 amps. If you are doing lazy circles in the sky, the amp draw will be significantly less. But if you are flying fast, doing high G manures, it’s something to keep in mind. The Rx will also draw a bit of power as well as anything else you might have hooked up.
As long as your total amp draw is below the ESC rating, you should be OK. Most of my fleet, the motor will draw 40-50 amps, I run 50-60 amp ESC’s.
You also need to be aware of the BEC rating. I fly hard and only buy ESC’s with a 4 amp or larger BEC’s
I buy the cheap ones, occasionally one of my ESC’s fail. I always keep a couple of spares on hand & just pop in a new one. Then place an order for a replacement and keep on flying while I wait on the slow boat to deliver my replacement.
...I'd guess it time dependent. (for #1) are the answers different for a 30 second burst and for full flight duration.
Yes to some extent, but it’s more on how accurate is the manufacturers rating. Believe it or not some manufacturers will overrate their ESC’s.
...If I were to put a thermistor and keep it under some max temperature, would this keep it from failing? Or are there other things beside burning up?
I don’t know, maybe, for me, that would be far more trouble than is is worth. If you have those kind of skills, try it and report back so we all can learn something new.