What does the ".cu" that appears at the end of domain names mean? For example in domain.cu?
It is the two-letter code assigned by the ISOC (Internet Society) as top level code for Cuba. Each country has a two-letter top level code.
Is it necessary for the server of a domain be registered under the same country identifier?
No. The server may be in any country.
What can I do if the domain name I want to register has already been registered?
If the top-level domain under .CU (myname.cu) has been registered, you can try to apply for a second-level domain under .cu (myname.com.cu). If this has also been registered, try looking for something to make it different, for example including a hyphen (my-name.cu) or a similar name or as a last resource, think of a another name.