PZ isn't an award booking code, it is an upgrade booking code. Booking code on the PNR isn't what the system looks at when crediting flights (it looks at the booking code of the fare on the ticket). And as others have mentioned, booking code doesn't matter when it's a UA operated segment as long as it isn't a bulk fare (which usually aren't upgradeable, and certainly not being sold on OA ticket stock) - all UA operated flights that aren't bulk earn based on $ spent, regardless of the ticketing carrier.

Also Lufthansa didn't do anything, what you're seeing is their website reflecting the changes that happened in the PNR based on messages sent from United's system. Which is your confirmed (HK) space in the premium cabin was cancelled (XK) since you were upgraded, which is why there is an additional status change message indicating you are confirmed (HK) in the business cabin.

Yes. For earnings purposes, the fare basis indicated in the individual ticket coupon is what drives the credit, not the booking code in the PNR.