Is it permissible to publish foreign videos that include women who are not wearing hijab or who are dressed immodestly, out of necessity, with no alternative available?

One must be cautious of video clips that contain images of unveiled women and seek out clips free from religious prohibitions. If such clips are not found and there is a need for these clips, then there is no harm in benefiting from them, because the presence of such images is a widespread affliction (عموم البلوى), and they are not intended for their own sake but rather the intention is to learn. Sheikh Ibn Uthaymeen was asked about the ruling on selling scientific books that contain images, and he differentiated between books whose primary purpose is the images—which are not permissible to buy—and books whose purpose is benefit and which contain incidental images—these are permissible to acquire and sell.