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...
DNS records are not copied automatically when you change nameservers. Your new DNS provider may offer an import feature, but you still need to check that every required record has been copied correctly.
Before switching, save your current configuration and set up the records for your website, email and service verification with the new provider. Check MX and TXT records as well as the records pointing to your website. Keep the old DNS zone active temporarily, where possible. If your domain uses DNSSEC, check separately what needs updating before changing the nameservers.