What is the maximum safe temperature that a brushless drone ESC should get? What could happen if a brushless ESC were to go over its maximum temperature tolerance?
Like you said in your answer, it does depend on the ESC... so you definitely want to look into the specifications for your particular components. However, to be safe, a good rule of thumb suggested on this forum is that you want to be able to put your finger on it without discomfort for five seconds. If your reflex is to withdraw after only 2 seconds, chances are you're running a significant risk of overheating it.
As to what happens if you exceed the temperature... it's not pretty. Insulation on electric components starts to melt, resulting in shorts... Overheating will typically result in a pretty instantaneous failure.
It's always a good idea to keep your ESC exposed to a constant airflow. If you put it inside a closed compartment, ensure that you have some way that airflow is being sent through that compartment.
It really depends on the ESC. Different ESC's have different ratings.
Many ESCs would perform best under 85°C and some microcontrollers work better if under 70°C. But there are ESCs that can work just fine with hotter temperatures. For example, Castle Creations ESCs can handle a sustained 70-82°C and will have issues around 100°C but most ESCs will have lower tolerance levels and may have issues above 80°C. In general, the closer an ESC is to room temperature, the better it's longevity will be.
If an ESC gets too hot, several things could happen that would result in it burning out. Some components of the ESC could stop functioning.
So the best thing you can do is look at the temperature ratings for the specific ESCs you are looking at and measure the temperature of the ESC after a flight. If the ESC is too hot you can set a throttle limit or adjust power in some way.
There is some more information here.