The documentation for the particular inverter you use should list the efficiency of the inverter. It's probably somewhere in the neighborhood of 85%-95% efficient. But to pick the correct inverter you need to add up the continuous power draw of all of the devices you plan to run off of it then pick an inverter that can source, continuously, at least that much power. You also may have some issues using a "standard" inverter which provides a very crude and digitally noisy approximation of a sine wave. The filtering in the monitors and server may be good enough to handle the noise, but you may also end up with artifacts. You won't necessarily know until you try it. For budget purposes you may want to figure the cost of a true sine wave inverter which is quite a bit more pricey than the psuedo sine version. Certainly if you're planning to have speakers powered by the inverter you'll want the pure sine inverter.
I don't have access to any charging system documentation for Skoda.
As for addressing the heat, is there maybe a liquid cooled heat exchanger option for the server you plan to use?
-Rod