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Each droplet is only assigned a single ipv4 address. This does not prevent hosting multiple domains using virtualhost configurations.
This depends on where you have pointed the nameservers for your domain. When you point your domain to a set of nameservers with your domain registrar you indicate what servers you want managing your DNS services. If you pointed your domain to ns1/2/3.digitalocean.com then you would manage your DNS via the DigitalOcean control panel. If you pointed it to nameserver names that you registered pointed at your zPanel installation then you would manage them via zPanel.