The whole display and fuel/washer light should all come on for a few seconds when the ignition is switched on then extinguish.

As said flashing means there is a problem with that part, i.e. open circuit so in your case as said the wiring is most likely at fault or the switch itself.

As to the headlight, assuming the light is actually working it's may be worth checking the correct bulb is fitted, that being H4 55/60W.

If it is, and you have a spare it's worth replacing, to see if this cures it, the system requires the correct bulbs to be fitted to work properly!

Martin