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...
No. DNS does not distinguish between uppercase and lowercase letters in domain names. For example, example.ro and Example.ro are the same domain, so you do not need to register them separately. You can use capital letters in promotional materials to make the name easier to read without creating a different domain.
However, the part of a web address after the domain may be treated differently by the server or application: /Contact and /contact can lead to different pages. If a full address does not work, check the spelling of the path as well as the domain. Keep the links you publish on your website consistent.