Does an internal examination require ghusl?
Ghusl isn't required for making internal examination; however, it invalidates one's fasting. And Allah Knows Best.
Is it a condition that a woman should untie her locks while making Ghusl (ritual bath)?
Ghusl from Janabah (ritual impurity), or menstruation obligates that water reaches the roots of the hair in order for the Ghusl to be valid, but if it doesn`t, then hair locks must be untied for water to reach them, and for Ghusl to become valid.
Is Making up Missed Obligatory Prayers an Obligation?
All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Missed obligatory prayer/prayers is a debt upon Muslim and making it up is an obligation, since the Prophet (PBUH) said: "pay the debt due to God, for it is the one which most deserves to be paid." [Agreed upon]. And Allah Knows Best.
How should I deal with the whispers of the devil with regard to ablution and purity?
Whispers in ablution are from the devil, and so you should take refuge in Allah from the devil`s evil suggestions that aim to distort the religion. Thus, once an organ is completely pure, don`t question its purity since having whispers doesn`t mean that the purity is invalid as it has already been established.