Is traveling for tourism considered a necessity that permits a man to photograph his wife and female محارم (unmarriageable kin), and what is the ruling on traveling to countries where open sins are prevalent without the ability to object to them or lower one's gaze from them?

It is absolutely impermissible to photograph women due to the resultant fitan (trials/temptations) and evils. A resolution has been issued by the Council of Senior Scholars prohibiting this. Similarly, traveling to non-Muslim countries and promiscuous lands is not permissible except in cases of extreme necessity, such as for medical treatment, trade, seeking knowledge unavailable in Muslim lands, or for Da‘wah (inviting to Islam). This is conditional upon being able to openly practice one's religion and avoid fitan. As for traveling merely for recreation and leisure, it is prohibited.