Does a woman losing herself by opening her labia to ensure no discharge that invalidates wudu has occurred, without touching the vulva, invalidate wudu? And is there another way to verify this?

Touching one's own private parts (vulva) invalidates ablution when the labia meet. However, touching beyond that point does not invalidate it. So, if you touch where the labia meet, your ablution is invalidated; otherwise, it is not. The secretions you feel are vaginal discharge, which is pure but invalidates ablution. The emission of female seminal fluid (maniy) necessitates ghusl (ritual bath). If you doubt whether something has exited, you are not required to investigate; rather, act upon certainty, which is the persistence of purity.