Cyprus is a remarkably safe country, with very little violent crime. Cars and houses frequently go unlocked. That said however, it is wise to be careful when accepting drinks from strangers, especially in Ayia Napa, since there have been numerous occasions of muggings. There also occasional residual hostility towards people of Turkish origin or appearance in the south side, so people of such origin are advised not to reveal it.
Note also that the numerous Cypriot "cabarets" are not what their name implies but rather brothels associated with organized crime.
talk
The official languages of Cyprus are Greek and Turkish. Greek is spoken predominately in the south and Turkish is spoken predominately in the north. English is very widely spoken by locals of all ages because of previous British rule. Other common languages spoken on the island are French, German and Russian.
respect
It is best to avoid discussion of the various merits of the Greek-Turkish divide and events beginning in 1963 in some quarters. Any sully of Archbishop Makarios will be looked down upon.
Internet access
Is increasingly available in tourist centres in the guise of internet cafes and side rooms equipped with monitors. prices vary, so shop about. 2 pounds an hour seems average, but you can do better. many cafes now offer free wi-fi access. most hotels and resorts now offer internet access to their guests under various arrangements.