I have a 2000 s500 engine just shut off by itself

Have the engine checked for vacuum leaks, that will cause a high idle speed. As a 35 year veteran of auto repair I can tell you that engine flushs are a 100% waste of your hard earned money.

is it an after market radio? if so it might not have enough power so it goes to pull power when its turned up and its not there so it just shuts off. try checking your radio wires and your fuse.

You may need a shop manual to get the wiring diagrams to troubleshoot this.
If that fuse powers the ASD relay, it handles the computer, the ignition coil, the injectors, and the O2 sensors.
The wiring diagrams I have show the fuses as numbered not named.

I think the first thing you should do is( SHUT THE ENGINE OFF) when you are fueling up. The engine running will cause static electricity, which can cause a spark to you fuel nozzel, then boom and you are burnt up along with your car. As to you running problem when fueling up, som cars have a sensor in the fue tank mesuring tank pressure. with the cap off there is no pressure

crank sensor

just went thru the same think wit a s 430 it was the crank position sensor . 60 bucks at auto zone and it took me 5min. 2 install if u need help feel free to call me 918 808 9706 chris

sounds like a fuel filter or more likely a fuel pump fault.low fuel transfer pressure,possibly a dealer would be cheaper than a diy repair unless you have the diagnosis correct.

You may have one of 2 things going on, first the AC compressor cycling switch ( located in the low pressure AC line) is sticking open, and the 2nd the field coil for the AC compressor clutch goes open when hot. When it quits get a 12 volt test light and see if the AC compressor has power to it. Hope this helps