What is the ruling on traveling to study—especially to study medicine—in a Muslim country like Turkey, without a mahram, and is there a difference between traveling alone or traveling with a group of Muslim girls?

It is more befitting for you to study in your own country and among your family, if you are secure regarding your religion and honor. You are not religiously obligated to supplicate against people. However, if you fear harm from studying with them and find an opportunity to study in an Islamic country, and you are in need of this study, then there is no harm in traveling there. If you do not find a mahram to accompany you and your stay in that country is safe, then it is permissible for you to travel without a mahram.