You can register .ro domains and every Romanian extension (.com.ro, .info.ro, .org.ro, .store.ro and more), plus international ones such as .com, .net, .org, .e...
Yes, you can use names such as ns1.example.ro for nameservers, but creating a DNS record alone is not enough. Those names must point to DNS servers configured to answer queries for the relevant domains.
If example.ro uses ns1.example.ro and ns2.example.ro as its own nameservers, glue records are also needed at the domain registry. These associate the nameserver names with their IP addresses so DNS resolution can begin. Check the procedure and extension requirements with your registrar before making changes. If you only want to connect a website to hosting, you generally do not need your own nameservers.