For how long must he fulfill his oath to prohibit his wife from traveling outside the country without his permission, after he intended for the prohibition to last "until Allah wills"?

Your statement to your wife: "You are threefold divorced if you contact outside the country we reside in" is a divorce suspended on a condition. If you intended a specific duration, the wording is restricted by it; otherwise, it is perpetual. The exception "half unspecified" is not valid unless certain conditions are met, including: that it is customarily connected to the original statement, and that you intended the exception before you finished the oath. If these conditions are not met and you did not have an intention for a specific duration, the divorce takes effect upon the wife's contact in the manner described. And does it count as three divorces? The majority of scholars hold that it does, while some scholars do not consider it to take effect unless there was an intention for divorce, then they differ on whether it counts according to the wording or as a single divorce.