A linear regulator such as the LD117V33 or LD117V5 will generate a lot of heat and will need a suitable heatsink. Why not use a DC DC converter like mini360 or mini560?
Of course, the fuse has to handle the full 1/2 amp. I'd use a 1A fuse, or higher. A fuse usually does its job AFTER something goes terribly wrong... If everything shorts-out the fuse will blow before wires start burning-up and hopefully before traces burn-off of the circuit board, etc.
There's an old joke... "The transistor blew to protect the fuse". But in reality, transistors usually short when they blow so the fuse goes too, but hopefully before a fire starts.
Good!
Maybe... If the TVS "kicks-in" you essentially get a short circuit and the fuse will blow. If blown fuses become a problem you're probably OK to take it out because the voltage regulator can probably handle a short-term spike. Or, you could look for a voltage regulator with a higher rating.
I'd go with at-least 1000uF. You MIGHT not need the voltage-drop protection because the processor will work as long as the voltage stays above about 3V. And, is it a problem if it resets during starting>
Some regulators require that, but I don't see it on the datasheet. If it's needed, it's because electrolytic capacitors don't "act like" capacitors at high frequencies and some regulators can go unstable and oscillate at MHz frequencies. It doesn't add anything to the "filtering".
If the ESP board runs on 5V, that's better because the more voltage you drop across the regulator the hotter it gets. (Watts = Voltage X Current, and any power dissipated by the regulator is converted to heat.) You may need a heatsink in any case.
I read buck converters like the Mini360 generate noise. Can I just put a capacitor at the 3.3V output to filter the noise? If yes, what capacitor(s) should I use?
For 5V it's for sure a good solution, but for 3.3V I cannot find a trustworthy car converter. I think also many cheap cigarette lighter chargers are of low quality and don't have proper protection.
I was not aware the a linear regulator converts all the voltage difference to heat, therefore I thought 250 mA is enough. I will therefore try 1A, that's also the maximum current for the 1N4007 diode.
I think it's fine if the fuse blow at 15V, it is a good warning for the owner that something is wrong with the car
If the voltage should anyway not drop below 10V (around 80% of voltage before start) or so during start or it will not start. Therefore, I expect the voltage output of the regulator will react quickly and therefore hold the voltage above 3V. There is no direct problem, but if an Arduino display with information like battery voltage and rpm gets black during start, it's not nice.
In the datasheet on page 3 they use 100 nF at the input and 10 µF at the output.
I want to use also a 3.3V display which needs around 300 mA and later other components. I think officially the ESP32 Dev Kit C does not support more than 50 mA current on the 3V3 pin: ESP32 DevKitC Pinout, Overview, Features & Datasheet. Later I want to use the ESP32-WROOM-32.
