What is the ruling on remaining in a place where there are transgressions, such as weddings where women's 'awrat are exposed or artificial eyelashes are worn? Is it sufficient to lower the gaze while offering admonition, or is it obligatory to leave?

If the celebration is free from forbidden acts such as singing, musical instruments, and intermingling, then there is no harm in attending it. The presence of women dressed in a manner that violates Islamic law does not prevent attendance, but one must lower their gaze and object to their attire.