I'm no expert in the field, but here are my thoughts...
If you intend to use a traditional full-service carrier, there is little reason to procure the phone privately. You will lose any real anonymity the moment that your SIM registers on the provider network. The carrier will obtain the phone's SIM and IMEI numbers, immediately associating them to your real identity.
If this is more about advertising privacy, simply purchasing your phone from Google
doesn't should not automatically associate your activities with the new phone to your Google identity. For that, you would need to log into the device with your Google account, or perform other tasks that would directly associate you to your Google account. For example, accessing websites that use Google sign-on services, or using credential-based apps with accounts that are previously associated to your Google identity.
Yes, as far as I understand it, airplane mode will effectively take your phone off the grid. I can't see how a carrier, even at the firmware level, would be able to switch the modem back on remotely.
I'm still working out the capabilities of a restricted Google Maps as well, so I can't comment on much here. Google Earth does require Google Services Framework in order to launch. Neither the Play Store nor Play Services are required for basic functionality, but navigation is not available without Location and Notifications being allowed under the app's permissions. As far as I can tell, you cannot download offline maps without signing into a Google account.
Hopefully someone with a bit more GrapheneOS experience can fully confirm some of these details.