Is there a way to generate power from the heat that would drive the electronics?
It is physically impossible to generate power from a single thermal source at a given temperature. This is a consequence of the second law of thermodynamics.
To generate power you need (at least) two systems at different temperature. Given the scenario you depicted, the higher temperature system would be the "ambient", so you need an accessible system at lower temperature. That would be the suit or some other thermally insulated container the fireman would carry with him. But as the power is generated, the "cooler" system would rise in temperature, so it is debatable for how long such a power generator would remain operative. In fact the power you could generate would decrease as the temperature difference between the two systems decreases. It all depends on the initial temperature of the "cooler" system, its thermal capacity and the amount of power you generate.
Moreover, the "cooler" system should be heavily thermally insulated from the ambient, otherwise it could get hotter much faster, still reducing its effective duration as the "cold source" for the power generator.
Related to your other questions this article about electronics for high temperatures might be interesting to you.
And here's a tutorial about electronics at extreme temperatures.
Particularly interesting is this section of the cited tutorial:
6) Why not use conventional electronics and keep it within its operating temperature range?
Conventional-temperature-range electronics can be used in an extreme-temperature environment by means of insulation and heating (for low-temperature environments) or refrigeration (for high-temperature environments). This can be combined with thermal sinks or thermal sources. For example, the well-logging electronics mentioned earlier may be placed in a dewar (vacuum-insulated vessel) to protect it from the hot environment. In addition, the electronics may be thermally connected to a thermal sink, a material that can absorb a large amount of heat without a substantial temperature increase. This is usually done by employing the material's phase change from solid to liquid, which absorbs a large amount of heat (the latent heat of fusion). For low temperature, the opposite effect may be used to provide a thermal source. The same material may serve as a thermal sink for high temperature or a thermal source for low temperature, and may be as basic as ice/water or less familiar such as a bismuth alloy.
Note: The terms thermal sink and thermal source are used here, but the terms heat sink and heat source are also used.
However, in many situations the techniques described above would be undesirable or impractical. There are trade-offs: the passive techniques may have a limited lifetime that is insufficient for the application. The active techniques require additional power and subsystems. For some applications, active techniques may be too disturbing to the environment because of the additional heat that must be dumped. All the techniques add weight, bulk, and some degree of complexity. These burdens may be less acceptable or less practical compared to using special electronics that can withstand the temperature of the environment. Thus, operating electronics beyond the normal limits is an option worth considering.
Moreover, this article seems mostly relevant and describes an "electronically enhanced" fireman suit and its abstract recites:
This article presents a system designed for monitoring the temperature in a textronic
fireman suit. The system consists of a set of sensors placed in the suit, a wireless connection sending the data to the main computer and a visualisation system. The article also focuses on software which enables to monitor the parameters of 30 firemen. The material presented illustrates contemporary problems occurring at the meeting point of three areas of knowledge: textile engineering, electronics and informatics.
