Is it permissible to attend a work iftar, a family group outing, or a farewell dinner that involves mixing between men and women, with the intention of representing the Muslim woman in her dress and manners?

Allah commanded men and women to lower their gaze, and prohibited seclusion and mixing that could lead to temptation. If a woman needs to travel, there is no harm in it, provided she is accompanied by her husband or a mahram (definition). If the purpose of these trips is that a woman is only present with a mahram, then there is no objection to them if they are for a need, while adhering to lowering the gaze and avoiding causes of temptation. The same applies for recreation, but it should not take up a long time.