Is the marriage considered valid if it took place after an illicit relationship that lasted two weeks, and with a prior intention to separate, in addition to the woman not observing an 'iddah of one menstrual cycle before the marriage?

If the pre-marital relationship did not reach the extent of fornication, then it has no effect on the validity of the marriage contract. If it did reach that extent, the marriage is not annulled. As for the wife's condition that she not leave her country, this is valid. However, if the intention is that she would separate from him through divorce if he leaves her country, then this condition invalidates the marriage contract.