Been through the boards for this, didn't see it exactly. Converting to VPS and the nameserver issues. Sooo... VPS is with Acme and our domain is with Registerfly.com. We set up nameservers with Registerfly (ns1 & ns2) to point to IPs with Acme...
Q1: Does it make any sense to setup and use a separate secondary name services for ns3 & ns4 like dnsmadeeasy.com seconaryt dns service... or some others: dyndns. org, zoneedit. com, ultradns. com
Q2: If Yes.. should we use a NEW domain hosted with another company for nameserver ( instead of current with Registerfly?)
If you have had DNS downtime or you are worried about redundancy then it is good to setup secondary DNS somewhere.
It does not matter if you use the same second level domain or two second level domains.
Using "mydomain2.com" and "mydomain.com" can just confuse some people so most people just use one domain (ns1-4.mydomain.com).