Does inserting a doctor's instrument or finger into a fasting woman's private parts during the day invalidate the fast, and is that considered masturbation with the discharge of white secretions, and does that necessitate making up the day? And does a woman have semen?

Inserting an endoscope or the physician's hand into a woman's private parts does not affect her fast, and it is not considered masturbation if it is for the purpose of a necessary medical examination. If something is discharged from the private parts as a result, then if it is maniy (seminal fluid), it invalidates the fast and necessitates making up the day; otherwise, it does not, unless its discharge was intentional with lust. Women have maniy similar to men's, and ghusl (ritual bath) is obligatory upon seeing it in a dream.