As far as ports, you should only need 53 and 22 open for this to work in APF. Make sure it's open from BOTH servers though.
As far as the other, you'll need to copy the entries that existed previously onto the new server and edit the named configuration files to read those as well.
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During sync between servers in a DNS cluster, the source server will use the 2087 port to sync zones. But, instead of leaving it wide open for -any- outgoing data through port 2087, you might want to drop the outgoing port 2087 from your conf.apf file, and instead add the target server's IP to the source server's apf allow host file under /etc/apf/allow_hosts.rules -- This will create a transparent firewall-trust relationship which will allow both servers to communicate through any port, so if cPanel later on decide to change port 2087 sync function to port XXXX it won't affect your server DNS sync function.