Electronic – How to get rid of vehicle voltage spikes maybe a choke and capacitor filter

I'm more for an RC-filter than an LC, and the resonance is one reason. You have a high noise suppression above the resonance frequency, but hardly anything below. If you then want a low cutoff-frequency the inductor may become impractically large.

I've seen circuits where EMI ferrite beads are used, but these are almost useless. They do have a near zero impedance at DC, but their peak impedance (often a few hundred ohms) often lies above 50 MHz, so much noise will hardly be filtered.

But the RC-filter isn't ideal: the resistor will have a voltage drop, and if you choose a low resistance you'll need a quite large capacitor to keep the low cutoff-frequency. An RC-filter may be acceptable if the microcontroller won't need much power (don't forget what it sources to its I/Os!), but at 5 mA a 100 Ω will already drop 500 mV, which is fine if the input voltage is chosen a bit high especially for this, but which you maybe can't afford.

Okay, assuming your question is about why the spikes are there and how to get rid it off...

If zero voltage switching is not used to synchronize the MOSFET switching with zero crossing of the rectified AC, switching occurs at random interval causing very high dV/dT and it generates tons of harmonics which adds up to the fundamental. Even if zvs is used, the MOSFET will have to cut off at non zero interval of the AC cycle since it follows the pwm signal from the controller. However, probably the severity of the harmonics could be reduced with zvs.

The only way to reduce this spikes is to employ snubber caps together with choke filters. Put the cap across the transformer primary just after a choke input filter. Caps may need resistor in series with them to prevent them from overheating.