Is it permissible to secretly marry a married man who refuses to inform his first wife of the marriage and stipulates that the second wife reside in another country far away from him?

If you are in need of marriage, there is no impediment to marrying this man, provided he proposes to your guardian (wali). It is advisable to verify his religiosity, character, and honesty. As for him leaving you for three or four months, there is no harm in it if it does not entail any danger or loss for you; the presence of a mahram will increase your safety. However, if it entails danger to you or if you fear fitna (temptation/strife), then do not agree. If you do agree, it is not permissible for him to leave you in this situation in the future; rather, he must take you with him, or escort you to a safe place, or arrange for a mahram to care for you until he returns. If he refuses, it is advisable to reject marrying him.