Comment by LinuxBender

How can you tell if a DNS server is already defined in the root anycast clusters?

One way is to query one of the root servers responsible for that TLD

If example.net, then adding extra steps to make it more explicit what's happening.

    # get the root servers for .net
    dig NS net
    net.   7 IN NS e.gtld-servers.net.
    [snip...]

    # just adding this step to make it more descriptive of whats happening
    dig +short e.gtld-servers.net
    192.12.94.30

    dig @192.12.94.30 +all +norecurse +nocookie -t ns example.net

    ;; AUTHORITY SECTION:
    example.net.  172800 IN NS a.iana-servers.net.
    example.net.  172800 IN NS b.iana-servers.net.
    [snip ... extra data ignored]

What's a good domain registry for an important domain? One where you own the domain, like Gandi, rather than just renting it from the domain registry, as with current NetSol terms?

All domains are rented. Premium registrars like MarkMonitor have monitoring options to see if someone managed to change the root servers for your domain and will try to fix it but I have no idea if they still do that or if they are still any good. They are meant for businesses.