Eastern Catholics follow the rest of the Catholic Church with regards to divorce and contraception. You are thinking of Eastern Orthodox. The Orthodox vary on this point. Divorce is permitted, but highly frowned upon (much more so than annulments in the Catholic Church). Also, divorce is an ecclesial matter. The divorce must be granted by the Church tribunal, not by your local JP. The reason that the Church can grant the divorce (in Orthodoxy) is that the Church is seen as the minister of the Sacrament of marriage, not the couple. This does not mean, however, the the marriage bond is broken. For the Orthodox faithful (as for Eastern Catholics) the marriage bond is eternal. Divorce, in the Orthodox tradition, is simply a recognition that the love which initially bound the two together has broken down beyond repair (due to lack of nurturing, human sinfulness, whatever). It provides the couple a way out of the marriage while still being in the good graces of the Church. It also provides them with a way to marry another and remain in the good graces of the Church. But, again, the divorce is granted by the Church, not the local JP. This actually makes it much more akin to the Catholic annulment process.
As far as contraception is concerned, the Orthodox are divided amongst themselves, particularly as it is seen as a non-dogmatic pastoral issue. Some Orthodox Churches permit contraception, and some are avidly against it. So it depends on who you talk to.
