Air carrier First Officer reported multiple anomalies on their international flight; including loss of one of their GPS systems and inability to log into Maastricht Control; apparently because the new aircraft was not yet registered in the system.

Narrative

The Captain and I came back from first break to take over for the second half of the flight. I was the pilot flying. We were over Europe and one of our GPS systems wasn't working and ADS-B was initially in and out. When appropriate; the Captain attempted to log on to CPDLC; but the system didn't recognize our aircraft. Maastricht Control confirmed that the airplane was new; and that our Company hadn't yet reported it for system registration. This meant we couldn't log on.We continued coordinating with ATC and we did manage to get an oceanic clearance; our assigned altitude was FL320 instead of the requested FL380. The Captain reached out to Dispatch; and we got a new flight plan. After some time and re-coordination; we climbed to FL360. Along the way; we received a few direct routings and level changes. At one point; a Controller asked us for our ANP (Actual Navigation Performance) compared to our RNP (Required Navigation Performance). We thought It was likely to ensure that we met the navigation accuracy requirements with the CPDLC not working.