How can I get divorced quickly and go back to my home in Europe,without hanging around in Israel,or Cyprus, if I am non-Jewish,and married a Jewish guy in a civil wedding in Cyprus,and he agrees to all this ?

By consenting to end the marriage, in writing,and, signing, a professionally drafted agreement concerning the dissolution of your marriage,which can be authorised by the family court in Israel,after your husband has also signed it.  You also need to sign a special, appropriate power of attorney allowing a lawyer to represent you,in Israel, during the proceedings,should you wish to return abroad meanwhile. You may also have to co-operate regarding the provision of information concerning your religious affiliation,as a technicality,depending on whether you belong to a religion recognised in Israel.

Mutual consent is sufficient grounds under Israeli law for ending a marriage between people of different religious affiliations,even if they married abroad,and one of them is a non-Israeli. Under Cypriot law foreigners who married in Cyprus must live over there for three months for a court in Cyprus to have jurisdiciton to deal with ending their marriage. Thus it is far easier and convenient for you to divorce via the Israeli legal system,but it is advisable to be represented by a specialist lawyer/attorney,in Israel, experienced at handling such cases.