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, some domains support accented and other non-ASCII characters. These are called internationalised domain names (IDNs), but the permitted characters depend on the extension and its registry rules. Before registering, check that your chosen extension allows the exact characters you want and that the name is available. Some interfaces may display the domain in its technical Punycode form, which starts with xn--.
The versions with and without diacritics are separate domains: registering one does not automatically reserve the other. If you also want to use the domain for email, check compatibility with your email service and applications, as support for these addresses can vary.