If there are 6V bulbs in the 12V system they'll be really bright for a short time until they burn out. Won't hurt anything but the bulb itself.
Switching to 12V from 6 volts requires new bulbs, flasher, maybe horn, and coil which would have been changed with the new engine. All the wiring and switches will be fine.
The white cover is the where the old air filter used to be. Makes a good storage space.