thanks
Cyprus is a country; Greece is a separate country.
So no; a visa for Greece will not work in Cyprus.
Depends on which kind of Visa do you have
First of all you should be aware of what is the Schengen Area
Schengen Area is the group of 26 european nations that have agreed to eliminate border control between them. In principle, any citizen of each country is allowed to live and move in any of the 26 countries.
Despite Cyprus not being yet in Schengen (your country has to achieve certain parameters of public safety, economic development, etc), it is already in a transition period, and Schengen nationals are allowed to enter as they are in the rest of the area.
For Schengen Visa holders it is the same, only depending on which type of Visa do you have, as some Visas are for one country only, while others allow you to travel accross all Schengen area. For more info, check the link below
http://www.schengenvisainfo.com/
Cyprus is an independent nation not related to the Greek government. If you need a visa to enter Greece then you probably need to apply for a Cypriot visa to enter Cyprus.
No.
However, a Greek residence permit would do.