Is a man required to renew the marriage contract after being absent from his wife for a year and a half, and is the wife required to observe 'iddah in this situation?

Divorce does not occur merely by the husband's absence, no matter how long it lasts. The wife is not required to observe an iddah (waiting period), nor does she need a new marriage contract, unless the husband divorces her, or performs khul‘ (dissolution of marriage at the wife's request), or a sharia ruling of divorce or annulment is issued.