It will not create any problem right if i remove default name servers from there.
No, and it’s the only way to make this work.
api.adpar.us should point our server.(A record)
No, you don’t need to manually create that A record. It will be handled by the registration server.
ns1.adpar.us should point our server.(NS name server for that domain)
Yes, the IP address of your registration server instance.