Regarding your first question, currently in GCP you can purchase your own domain using Cloud Domains and you can export/migrate it to a different registrar, but it is not possible (at this moment) to import a domain as described here:
Note: Cloud Domains does not currently support incoming transfers or
import of domains. You can make outgoing transfers to Google Domains
or other registrars directly in Cloud Domains.
Nevertheless, you can delegate the control of your domain to Cloud DNS (or any other DNS provider like GoDaddy) which is also offered in GCP, for that you need to create a new zone in your project for your domain, and you will receive some instructions and nameserver (NS) records. Then you need to replace/update your NS records in your registrar (Google Domains in this case) for those provided by Cloud DNS and wait some time until the propagation is finished, here is the official guide about this, but you can find some useful guides on the Internet for your particular use case. This way you can manage your domain from the GCP Console but take into consideration that this is only a delegation, the registrar will still be Google Domains, if by any reason you update your NS records in Google Domains (pointing to a different DNS provider), any change in Cloud DNS will not be effective anymore.