A resistor will produce a voltage drop, but not a regulated voltage. The simple way to build a regulated 5V source is with a 7805.

To wire a relay that's energized in either the accessory or run position, you need to tap a circuit that's powered in either the accessory or run position...so why are we talking about fuel pump and Klima, which aren't powered in accessory? Further, the fuel pump relay is eliminated in a diesel conversion and the Klima circuit would be rewired. How about the radio or lighter? That takes care of energizing the coil. The contacts should be powered directly from the battery, with an inline fuse, or you could used a fused relay.

Why are you going about things in this odd way? Any electronic equipment you buy will run on 12V and handle it's own voltage regulation. And if you were capable of developing your own electronics, you wouldn't be asking these questions.