Is it permissible to travel for study in a Western country, knowing that study in its universities is mixed? And is the need considered available in this case? And what is the ruling on obtaining health insurance to acquire a transit visa?

If you are able to manifest the rituals of your religion and are safe from fitna concerning your faith, and you adhere to the Sharia guidelines for studying in mixed universities in Western countries, then your study there is permissible. The high cost of studying in your own country and the poor conditions in other countries excuse your travel to study in the West, provided you adhere to the aforementioned guidelines. There is no objection to the mandatory health insurance requirement, but if you find cooperative insurance, then it is not permissible for you to subscribe to commercial insurance.