1. 'Default IP' as the name suggests is default IP address of the zone. If you don't specify an IP adress when you create a new zone, default IP will be used. In case you don't provide default IP neither zone IP, you won't be able to create new zone.
2. 'Name' in PowerDNS module 'Connection' tab is the field called 'name' in the SOA record. This record is added when the zone is created. You can define SOA record format in the configuration of the module. Available variables are {$domain} and {$ip} in fields: 'Name' , 'Primary' , 'Hostmaster' .