Do iPhone chargers need any certification to correctly work? Since lightning cables need MFi certification, I would like to know if wall (and car) chargers need this or any certification too to get all features like fast charging.
It is not necessary that the charger is MFI certified to work at all, nor is it necessary to get fast charging working. Depending on the model of your iPhone and iPad, you can use a standard USB-C charger to charge the device - fast or slow.