Hi Keruru. Your budgie is really cute! I love the colors.
The beak grinding thing, I know they will do that when they are about to go to sleep, perhaps there are other situations when they do that. I took it to mean they are feeling comfy and happy. Thinking about it now, mine do that too at odd times. A clicking noise and grinding.
The head thing, it may be just a weird little thing. Mine sometimes move their heads around, like they're doing the "robot" dance! i don't know how else to say it. lol Maybe someone else on here has some info to give us!