Is Cyprus a schengen country?
No. Cyprus is not part of the Schengen Area.
No, Northern Cyprus is not a member of the Schengen Agreement. Northern Cyprus is not recognised as an independent country by any other country except Turkey, the rest of the world thinks the whole of Cyprus belongs legally to the Republic of Cyprus. As an unrecognised country no other country will sign treaties with it, Schengen or any other treaty.
Is Greek Cyprus one of the Schengen states. If not so then about how much time will it take to be one of the Schengen states?
According to the EU-Cyprus Accession Treaty, Cyprus is required to eventually join the Schengen Area. However, the current "border arrangement" that Cyprus has with the illegitimate Turkish Republic of Northern Cyprus is a serious stumbling block to implementing the border security requirements necessary for Schengen. As a result, the earliest that Cyprus may be able to join Schengen will be in 2016, but likely will not happen for many more years.
Ireland, The United Kingdom, Croatia, Romania, Cyprus and Bulgaria are all EU countries that are not members of the Schengen area. Croatia, Romania, Cyprus and Bulgaria will join at some future date, while Ireland and the United Kingdom have an opt-out and they also have their own common travel area.